tested hypotheses

things to do

install and load supporting libraries

##        nodename 
## "stp-air.local"
## [1] "R version 3.2.3 (2015-12-10)"
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
## 
##     select
## 
## 'drc' has been loaded.
## Please cite R and 'drc' if used for a publication,
## for references type 'citation()' and 'citation('drc')'.
## Loading required package: lme4
## Loading required package: Matrix
## [1] "list of loaded packages: "
##  [1] "pbkrtest"      "lme4"          "Matrix"        "scatterplot3d"
##  [5] "ggplot2"       "drc"           "MASS"          "xtable"       
##  [9] "zoo"           "knitr"         "dplyr"         "rmarkdown"    
## [13] "stats"         "graphics"      "grDevices"     "utils"        
## [17] "datasets"      "methods"       "base"

import experimental exposure and microsomal data

Load csv files with experimental data and microsome data sets. The beolw may return false but still be OK if rstudio does not have privileges to data directory (e.g., attached drive).

## [1] "Root directory location: /Users/puruckertom/git/glinski_metabolites/"
## [1] "check to see if R can access files OK: TRUE"

experimental exposure data structure

Check out structure of imported data sets.

str(micro)
## 'data.frame':    352 obs. of  6 variables:
##  $ time     : int  2 2 2 2 4 4 4 4 12 12 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  3.07 3.69 4.7 1.89 7.62 ...
##  $ replicate: int  1 2 3 4 1 2 3 4 1 2 ...

Set time and replicate fields as factors for later statistical inference.

microsome experiment data structure

Check out structure of imported data set for the microsome analysis.

str(microsome)
## 'data.frame':    1123 obs. of  7 variables:
##  $ time     : int  0 0 0 15 15 15 30 30 30 60 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  1.208 1.596 1.362 0.551 1.347 ...
##  $ replicate: int  1 2 3 1 2 3 1 2 3 1 ...
##  $ microMexp: num  0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...

Set time and replicate fields as factors for later statistical inference.

## 'data.frame':    1123 obs. of  7 variables:
##  $ time     : int  0 0 0 15 15 15 30 30 30 60 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  1.208 1.596 1.362 0.551 1.347 ...
##  $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 1 2 3 1 2 3 1 ...
##  $ microMexp: num  0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...

analyze microsomal data

The microsomal experiment has 3-4 replicates for each pesticide. The experiment progressively increases the concentration of the substrate (microMexp) and measures the enzyme velocity. At each substrate concentration the reaction is quenched after a specific period of time (0, 15, 30, 60, 90 mins). This time series data is used to estimate a slope associated with each substrate concentration. Substrate concentration and linear velocity slopes are then fit using Michaelis-Menten kinetics to estimate reaction rates for each pesticide.

non-linear fitting

We use the dose-response model (drm) package from R for the fitting of the rate constant. We provide it the 2-parameter Michaelis-Menton function (mm2) as an argument. It uses the MM.2 function that is in the drc package and therefore is a drc object that contains a list of class drcMean, containing the mean function, the self starter function, the parameter names and other components such as derivatives and a function for calculating ED values. It is not shifted (??) so uses the fit f(x,(c,d,e)) = c + (d-c)/(1+e/x). Where x is the dose, it is a strictly increasing function so we reverse the sign of the slopes for the parents. e is the dose halfway between c and d, for the 2-parameter model c = 0.

## Michaelis-Menten 
## (2 parameters) 
## In 'drc':  MM.2

atrazine

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.712"
##       ind             
##  [1,]   1  0 0.7120000
##  [2,]   2  0 0.7120000
##  [3,]   3  0 0.7120000
##  [4,]   4 15 0.5514354
##  [5,]   5 15 1.3469113
##  [6,]   6 15 1.2124448
##  [7,]   7 30 1.1349183
##  [8,]   8 30 1.0824669
##  [9,]   9 30 1.1138895
## [10,]  10 60 0.9180152
## [11,]  11 60 0.8199161
## [12,]  12 60 0.8304017
## [13,]  13 90 0.6019329
## [14,]  14 90 0.5146155
## [15,]  15 90 0.5430465
## [1] "least squares linear regression for substrate = 0.712"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    0.976685    -0.003153  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.37796 -0.22151  0.03239  0.21607  0.41752 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.976685   0.103348   9.450 3.45e-07 ***
## Time[ind]   -0.003153   0.002041  -1.545    0.146    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2554 on 13 degrees of freedom
## Multiple R-squared:  0.1551, Adjusted R-squared:  0.09013 
## F-statistic: 2.387 on 1 and 13 DF,  p-value: 0.1463
## 
##  (Intercept)    Time[ind] 
##  0.976685382 -0.003152627 
##                    2.5 %      97.5 %
## (Intercept)  0.753415733 1.199955031
## Time[ind]   -0.007561078 0.001255824

## [1] "weighted linear regression for substrate = 0.712"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
##  (Intercept)    Time[ind] 
##  0.976685382 -0.003152627 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.344 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.37796 -0.22151  0.03239  0.21607  0.41752 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.9767  0.1033     9.4505
## Time[ind]   -0.0032  0.0020    -1.5450
## 
## Residual standard error: 0.3436 on 13 degrees of freedom

##  (Intercept)    Time[ind] 
##  0.976685382 -0.003152627 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##       ind             
##  [1,]  16  0 10.000000
##  [2,]  17  0 10.000000
##  [3,]  18  0 10.000000
##  [4,]  19 15  8.453643
##  [5,]  20 15  7.964608
##  [6,]  21 15  7.944511
##  [7,]  22 30  7.680602
##  [8,]  23 30  7.527337
##  [9,]  24 30  7.478498
## [10,]  25 60  5.659398
## [11,]  26 60  6.364134
## [12,]  27 60  6.660240
## [13,]  28 60  6.342496
## [14,]  29 90  5.477249
## [15,]  30 90  5.670032
## [1] "least squares linear regression for substrate = 10"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##      9.3056      -0.0475  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.7963 -0.3777 -0.1132  0.5429  0.6944 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  9.305616   0.225240   41.31 3.53e-15 ***
## Time[ind]   -0.047498   0.004733  -10.04 1.73e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5487 on 13 degrees of freedom
## Multiple R-squared:  0.8857, Adjusted R-squared:  0.8769 
## F-statistic: 100.7 on 1 and 13 DF,  p-value: 1.726e-07
## 
## (Intercept)   Time[ind] 
##  9.30561649 -0.04749819 
##                   2.5 %      97.5 %
## (Intercept)  8.81901420  9.79221878
## Time[ind]   -0.05772265 -0.03727374

## [1] "weighted linear regression for substrate = 10"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  9.30561649 -0.04749819 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.662 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.7963 -0.3778 -0.1132  0.5429  0.6944 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept)   9.3056   0.2252    41.3142
## Time[ind]    -0.0475   0.0047   -10.0361
## 
## Residual standard error: 0.6619 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  9.30561649 -0.04749819 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  3.1684"
##       ind            
##  [1,]  31  0 3.168400
##  [2,]  32  0 3.168400
##  [3,]  33  0 3.168400
##  [4,]  34 15 3.840289
##  [5,]  35 15 3.471244
##  [6,]  36 15 4.218922
##  [7,]  37 30 3.041496
##  [8,]  38 30 3.107057
##  [9,]  39 30 2.539792
## [10,]  40 60 2.350741
## [11,]  41 60 2.184286
## [12,]  42 60 1.868857
## [13,]  43 90 1.487945
## [14,]  44 90 1.746449
## [15,]  45 90 1.279189
## [1] "least squares linear regression for substrate = 3.1684"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     3.60836     -0.02305  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.43996 -0.36681 -0.04111  0.19940  0.95630 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.608360   0.171081  21.091 1.94e-11 ***
## Time[ind]   -0.023049   0.003378  -6.823 1.22e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4227 on 13 degrees of freedom
## Multiple R-squared:  0.7817, Adjusted R-squared:  0.7649 
## F-statistic: 46.56 on 1 and 13 DF,  p-value: 1.218e-05
## 
## (Intercept)   Time[ind] 
##  3.60836007 -0.02304946 
##                   2.5 %      97.5 %
## (Intercept)  3.23876147  3.97795868
## Time[ind]   -0.03034717 -0.01575175

## [1] "weighted linear regression for substrate = 3.1684"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##   3.5347402  -0.0221571 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.399 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.36634 -0.33335 -0.02103  0.22144  1.01654 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  3.5347  0.1617    21.8588
## Time[ind]   -0.0222  0.0032    -6.9395
## 
## Residual standard error: 0.3986 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##   3.5347402  -0.0221571 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##       ind            
##  [1,]  46  0 50.00000
##  [2,]  47  0 50.00000
##  [3,]  48  0 50.00000
##  [4,]  49 15 30.13526
##  [5,]  50 15 28.31361
##  [6,]  51 15 26.04382
##  [7,]  52 30 30.34766
##  [8,]  53 30 27.74702
##  [9,]  54 30 25.64127
## [10,]  55 60 28.51624
## [11,]  56 60 26.35221
## [12,]  57 60 24.78296
## [13,]  58 90 26.56519
## [14,]  59 90 24.44743
## [15,]  60 90 24.01566
## [1] "least squares linear regression for substrate = 50"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##       39.33        -0.20  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.2839  -5.8864  -0.9746   4.1802  10.6720 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 39.32803    2.97479  13.220 6.49e-09 ***
## Time[ind]   -0.20002    0.05874  -3.405  0.00469 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.35 on 13 degrees of freedom
## Multiple R-squared:  0.4715, Adjusted R-squared:  0.4308 
## F-statistic:  11.6 on 1 and 13 DF,  p-value: 0.004694
## 
## (Intercept)   Time[ind] 
##  39.3280334  -0.2000208 
##                  2.5 %      97.5 %
## (Intercept) 32.9013986 45.75466818
## Time[ind]   -0.3269145 -0.07312715

## [1] "weighted linear regression for substrate = 50"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  39.3280334  -0.2000208 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 8.27 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.2839  -5.8864  -0.9746   4.1802  10.6720 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 39.3280  2.9748    13.2205
## Time[ind]   -0.2000  0.0587    -3.4054
## 
## Residual standard error: 8.273 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  39.3280334  -0.2000208 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##       ind            
##  [1,]  61  0 75.00000
##  [2,]  62  0 75.00000
##  [3,]  63  0 75.00000
##  [4,]  64 15 29.59549
##  [5,]  65 15 36.16487
##  [6,]  66 15 37.40302
##  [7,]  67 30 27.64656
##  [8,]  68 30 28.94211
##  [9,]  69 30 34.71956
## [10,]  70 60 31.19094
## [11,]  71 60 35.96712
## [12,]  72 60 33.12001
## [13,]  73 90 31.51870
## [14,]  74 90 32.99096
## [15,]  75 90 22.85693
## [1] "least squares linear regression for substrate = 75"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     54.1995      -0.3519  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -19.325 -12.137   0.036   9.729  20.800 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  54.1995     5.8549   9.257 4.37e-07 ***
## Time[ind]    -0.3519     0.1156  -3.044   0.0094 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.47 on 13 degrees of freedom
## Multiple R-squared:  0.4162, Adjusted R-squared:  0.3713 
## F-statistic: 9.267 on 1 and 13 DF,  p-value: 0.009404
## 
## (Intercept)   Time[ind] 
##  54.1995284  -0.3519259 
##                 2.5 %     97.5 %
## (Intercept) 41.550828 66.8482288
## Time[ind]   -0.601674 -0.1021778

## [1] "weighted linear regression for substrate = 75"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  54.1995284  -0.3519259 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 17.1 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -19.32515 -12.13669   0.03604   9.72863  20.80047 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 54.1995  5.8549     9.2572
## Time[ind]   -0.3519  0.1156    -3.0442
## 
## Residual standard error: 17.08 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  54.1995284  -0.3519259 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##       ind             
##  [1,]  76  0 100.00000
##  [2,]  77  0 100.00000
##  [3,]  78  0 100.00000
##  [4,]  79 15  73.12306
##  [5,]  80 15  62.97208
##  [6,]  81 15  58.17492
##  [7,]  82 30  70.93575
##  [8,]  83 30  60.89976
##  [9,]  84 30  54.39425
## [10,]  85 60  67.30937
## [11,]  86 60  56.75248
## [12,]  87 60  50.73569
## [13,]  88 90  64.11432
## [14,]  89 90  53.06961
## [15,]  90 90  51.00465
## [1] "least squares linear regression for substrate = 100"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##     82.6524      -0.3697  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.9313 -10.1962  -0.6243  10.7902  17.3476 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  82.6524     5.3532  15.440 9.66e-10 ***
## Time[ind]    -0.3697     0.1057  -3.498  0.00393 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.23 on 13 degrees of freedom
## Multiple R-squared:  0.4849, Adjusted R-squared:  0.4453 
## F-statistic: 12.24 on 1 and 13 DF,  p-value: 0.003928
## 
## (Intercept)   Time[ind] 
##  82.6523916  -0.3697435 
##                  2.5 %     97.5 %
## (Intercept) 71.0875829 94.2172003
## Time[ind]   -0.5980902 -0.1413968

## [1] "weighted linear regression for substrate = 100"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  82.6523916  -0.3697435 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 15.8 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.9313 -10.1962  -0.6243  10.7902  17.3476 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 82.6524  5.3532    15.4399
## Time[ind]   -0.3697  0.1057    -3.4981
## 
## Residual standard error: 15.8 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  82.6523916  -0.3697435 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##       ind             
##  [1,]  91  0 125.00000
##  [2,]  92  0 125.00000
##  [3,]  93 15 107.97377
##  [4,]  94 15  85.24148
##  [5,]  95 15  85.54902
##  [6,]  96 30 158.65079
##  [7,]  97 30  83.63860
##  [8,]  98 30  83.07468
##  [9,]  99 60 170.65218
## [10,] 100 60  78.21162
## [11,] 101 60  84.54186
## [12,] 102 90  80.88479
## [13,] 103 90  79.00425
## [14,] 104 90  78.20108
## [1] "least squares linear regression for substrate = 125"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    114.3266      -0.2991  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -24.599 -20.830  -8.809   7.538  74.269 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 114.3266    13.6528   8.374 2.35e-06 ***
## Time[ind]    -0.2991     0.2604  -1.148    0.273    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 30.85 on 12 degrees of freedom
## Multiple R-squared:  0.099,  Adjusted R-squared:  0.02392 
## F-statistic: 1.319 on 1 and 12 DF,  p-value: 0.2732
## 
## (Intercept)   Time[ind] 
## 114.3266319  -0.2990577 
##                  2.5 %      97.5 %
## (Intercept) 84.5797002 144.0735637
## Time[ind]   -0.8664937   0.2683783

## [1] "weighted linear regression for substrate = 125"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 110.3197856  -0.3413573 
## 
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 21.8 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -19.958 -15.237  -0.995  11.704  80.814 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept) 110.3198   9.2531    11.9224
## Time[ind]    -0.3414   0.1765    -1.9339
## 
## Residual standard error: 21.76 on 12 degrees of freedom

## (Intercept)   Time[ind] 
## 110.3197856  -0.3413573 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##       ind             
##  [1,] 105  0 150.00000
##  [2,] 106  0 150.00000
##  [3,] 107  0 150.00000
##  [4,] 108  0 150.00000
##  [5,] 109 15 110.80503
##  [6,] 110 15 114.72056
##  [7,] 111 15 107.12911
##  [8,] 112 15 110.21111
##  [9,] 113 30 106.41140
## [10,] 114 30 109.25884
## [11,] 115 30 108.81109
## [12,] 116 30  98.45122
## [13,] 117 60 105.73976
## [14,] 118 60 103.55787
## [15,] 119 60 109.56959
## [16,] 120 60 103.20775
## [17,] 121 90  96.26534
## [18,] 122 90 104.97418
## [19,] 123 90 105.79428
## [20,] 124 90  95.31462
## [1] "least squares linear regression for substrate = 150"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    130.2975      -0.4048  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -19.703 -10.065  -1.362  11.312  19.703 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 130.29755    4.74893  27.437 3.87e-16 ***
## Time[ind]    -0.40478    0.09377  -4.317 0.000415 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.55 on 18 degrees of freedom
## Multiple R-squared:  0.5087, Adjusted R-squared:  0.4814 
## F-statistic: 18.64 on 1 and 18 DF,  p-value: 0.0004153
## 
## (Intercept)   Time[ind] 
## 130.2975485  -0.4047811 
##                   2.5 %      97.5 %
## (Intercept) 120.3204116 140.2746854
## Time[ind]    -0.6017793  -0.2077829

## [1] "weighted linear regression for substrate = 150"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 130.2975485  -0.4047811 
## 
## Degrees of freedom: 20 total; 18 residual
## Scale estimate: 16.9 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -19.703 -10.065  -1.362  11.312  19.702 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept) 130.2975   4.7489    27.4372
## Time[ind]    -0.4048   0.0938    -4.3169
## 
## Residual standard error: 16.94 on 18 degrees of freedom

## (Intercept)   Time[ind] 
## 130.2975485  -0.4047811 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##       ind            
##  [1,] 125  0 200.0000
##  [2,] 126  0 200.0000
##  [3,] 127  0 200.0000
##  [4,] 128 15 200.8988
##  [5,] 129 15 134.8156
##  [6,] 130 15 211.5786
##  [7,] 131 30 193.1223
##  [8,] 132 30 210.4726
##  [9,] 133 30 213.5141
## [10,] 134 60 197.4426
## [11,] 135 60 146.8087
## [12,] 136 60 201.9011
## [13,] 137 90 127.9031
## [14,] 138 90 203.6292
## [15,] 139 90 128.0068
## [1] "least squares linear regression for substrate = 200"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    202.5624      -0.4587  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -60.866 -15.397   4.321  22.037  42.350 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 202.5624    11.8464  17.099 2.72e-10 ***
## Time[ind]    -0.4587     0.2339  -1.961   0.0717 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29.27 on 13 degrees of freedom
## Multiple R-squared:  0.2283, Adjusted R-squared:  0.1689 
## F-statistic: 3.846 on 1 and 13 DF,  p-value: 0.07165
## 
## (Intercept)   Time[ind] 
## 202.5623712  -0.4587044 
##                   2.5 %       97.5 %
## (Intercept) 176.9698580 228.15488441
## Time[ind]    -0.9640276   0.04661879

## [1] "weighted linear regression for substrate = 200"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 205.0357007  -0.4886842 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 32.2 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -62.890 -16.971   2.747  20.913  42.575 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept) 205.0357  11.5896    17.6913
## Time[ind]    -0.4887   0.2288    -2.1355
## 
## Residual standard error: 32.21 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 205.0357007  -0.4886842 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##       ind            
##  [1,] 140  0 250.0000
##  [2,] 141  0 250.0000
##  [3,] 142  0 250.0000
##  [4,] 143 15 111.0650
##  [5,] 144 15 110.3942
##  [6,] 145 15 107.7700
##  [7,] 146 30 110.0390
##  [8,] 147 31 133.1637
##  [9,] 148 30 106.6453
## [10,] 149 60 125.4094
## [11,] 150 60 132.3152
## [12,] 151 60 129.5529
## [13,] 152 90 107.9475
## [14,] 153 90 109.2892
## [15,] 154 90 110.9269
## [1] "least squares linear regression for substrate = 250"
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Coefficients:
## (Intercept)    Time[ind]  
##    181.5297      -0.9871  
## 
## 
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -58.954 -43.575   7.248  17.415  68.470 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 181.5297    19.1185   9.495 3.27e-07 ***
## Time[ind]    -0.9871     0.3772  -2.617   0.0213 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 47.18 on 13 degrees of freedom
## Multiple R-squared:  0.345,  Adjusted R-squared:  0.2946 
## F-statistic: 6.848 on 1 and 13 DF,  p-value: 0.02131
## 
## (Intercept)   Time[ind] 
## 181.5296510  -0.9870757 
##                  2.5 %     97.5 %
## (Intercept) 140.226690 222.832612
## Time[ind]    -1.801955  -0.172196

## [1] "weighted linear regression for substrate = 250"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 181.5296510  -0.9870757 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 62.1 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -58.954 -43.575   7.248  17.415  68.470 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept) 181.5297  19.1185     9.4950
## Time[ind]    -0.9871   0.3772    -2.6169
## 
## Residual standard error: 62.09 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 181.5296510  -0.9870757 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## 'data.frame':    10 obs. of  2 variables:
##  $ sub: num  0.712 10 3.168 50 75 ...
##  $ vel: num  15.8 237.5 110.8 1000.1 1759.6 ...
##         sub        vel
## 1    0.7120   15.76313
## 2   10.0000  237.49097
## 3    3.1684  110.78549
## 4   50.0000 1000.10406
## 5   75.0000 1759.62962
## 6  100.0000 1848.71748
## 7  125.0000 1706.78667
## 8  150.0000 2023.90534
## 9  200.0000 2443.42089
## 10 250.0000 4935.37833

## [1] "here are the rates"
## 
## Model fitted: Michaelis-Menten (2 parms)
## 
## Parameter estimates:
## 
##                 Estimate Std. Error    t-value p-value
## d:(Intercept) 1.1875e+05 2.9122e+05 4.0778e-01  0.6941
## e:(Intercept) 7.0431e+03 1.7722e+04 3.9742e-01  0.7015
## 
## Residual standard error:
## 
##  513.6883 (8 degrees of freedom)

We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.

We are fitting the 2-parameter model.

Used to estimate slopes.

dea

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.105334715" "Concs = 0.177716074" "Concs = 0.215668236"
##  [7] "Concs = 0.273065521" "Concs = 0.362248011" "Concs = 0.403265809"
## [10] "Concs = 0.502168642" "Concs = 0.64289193"  "Concs = 0.720570734"
## [13] "Concs = 0.725802164" "Concs = 0.865500124" "Concs = 0.956691847"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 8 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 0.023932957 0.009657919 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0695 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.16734 -0.03413 -0.02393  0.04772  0.11716 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.0239  0.0333     0.7179
## Time[ind]    0.0097  0.0007    14.6730
## 
## Residual standard error: 0.06948 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 0.023932957 0.009657919 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.062527948" "Concs = 0.066722432" "Concs = 0.073739184"
##  [7] "Concs = 0.13417786"  "Concs = 0.142144514" "Concs = 0.153899766"
## [10] "Concs = 0.359398841" "Concs = 0.284549411" "Concs = 0.293488967"
## [13] "Concs = 0.291970799" "Concs = 0.378114427" "Concs = 0.405964967"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 0.002435634 0.004635853 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0109 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.041548 -0.006292 -0.002436  0.007673  0.078812 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.0024  0.0048     0.5086
## Time[ind]    0.0046  0.0001    46.0686
## 
## Residual standard error: 0.01087 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 0.002435634 0.004635853 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.692469949" "Concs = 0.598237597" "Concs = 0.603481745"
##  [7] "Concs = 1.23886552"  "Concs = 1.156190328" "Concs = 1.011651128"
## [10] "Concs = 2.056702931" "Concs = 1.850305243" "Concs = 1.516060546"
## [13] "Concs = 2.637550555" "Concs = 2.271829323" "Concs = 2.15464298" 
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##   0.1946066   0.0254169 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.289 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.32748 -0.19461  0.02762  0.14305  0.33708 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.1946  0.0868     2.2415
## Time[ind]    0.0254  0.0017    14.8270
## 
## Residual standard error: 0.2885 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##   0.1946066   0.0254169 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59" "Indices =  60"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.126910879" "Concs = 0.194298986" "Concs = 0.205689666"
##  [7] "Concs = 0.343048244" "Concs = 0.344665429" "Concs = 0.433300567"
## [10] "Concs = 0.79823473"  "Concs = 0.910129645" "Concs = 0.789753599"
## [13] "Concs = 1.097803094" "Concs = 1.250836941" "Concs = 0.891346428"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 11 iterations
## 
## Coefficients:
##  (Intercept)    Time[ind] 
## -0.004886745  0.012957863 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0581 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.269974 -0.039992  0.004887  0.021409  0.137545 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) -0.0049  0.0265    -0.1845
## Time[ind]    0.0130  0.0005    24.7777
## 
## Residual standard error: 0.05809 on 13 degrees of freedom

##  (Intercept)    Time[ind] 
## -0.004886745  0.012957863 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  61" "Indices =  62" "Indices =  63" "Indices =  64"
##  [5] "Indices =  65" "Indices =  66" "Indices =  67" "Indices =  68"
##  [9] "Indices =  69" "Indices =  70" "Indices =  71" "Indices =  72"
## [13] "Indices =  73"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.660583406" "Concs = 0.521827731" "Concs = 0.519014334"
##  [7] "Concs = 0.937060708" "Concs = 0.947234926" "Concs = 1.586433592"
## [10] "Concs = 1.701961252" "Concs = 2.098184546" "Concs = 2.114078113"
## [13] "Concs = 1.9947066"  
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.15066966  0.02246945 
## 
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.182 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.1782 -0.1507  0.0313  0.1123  0.2031 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.1507  0.0584     2.5779
## Time[ind]    0.0225  0.0011    19.6538
## 
## Residual standard error: 0.1816 on 11 degrees of freedom

## (Intercept)   Time[ind] 
##  0.15066966  0.02246945 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  0.712"
##  [1] "Indices =  74" "Indices =  75" "Indices =  76" "Indices =  77"
##  [5] "Indices =  78" "Indices =  79" "Indices =  80" "Indices =  81"
##  [9] "Indices =  82" "Indices =  83" "Indices =  84" "Indices =  85"
## [13] "Indices =  86" "Indices =  87"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##  [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 0 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##           0           0 
## 
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##    Min     1Q Median     3Q    Max 
##      0      0      0      0      0 
## 
## Coefficients:
##             Value Std. Error t value
## (Intercept)   0   NaN        NaN    
## Time[ind]     0   NaN        NaN    
## 
## Residual standard error: 0 on 12 degrees of freedom

## (Intercept)   Time[ind] 
##           0           0 
##             2.5 % 97.5 %
## (Intercept)   NaN    NaN
## Time[ind]     NaN    NaN
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  3.1684"
##  [1] "Indices =  88"  "Indices =  89"  "Indices =  90"  "Indices =  91" 
##  [5] "Indices =  92"  "Indices =  93"  "Indices =  94"  "Indices =  95" 
##  [9] "Indices =  96"  "Indices =  97"  "Indices =  98"  "Indices =  99" 
## [13] "Indices =  100" "Indices =  101" "Indices =  102"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0"           "Concs = 0"           "Concs = 0"          
## [10] "Concs = 0.004276181" "Concs = 0"           "Concs = 0"          
## [13] "Concs = 0.068958259" "Concs = 0.095246481" "Concs = 0.042564751"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 16 iterations
## 
## Coefficients:
##   (Intercept)     Time[ind] 
## -0.0090857770  0.0005150538 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0135 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.021817 -0.006366  0.001360  0.009086  0.057977 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) -0.0091  0.0072    -1.2543
## Time[ind]    0.0005  0.0001     3.6012
## 
## Residual standard error: 0.01347 on 13 degrees of freedom

##   (Intercept)     Time[ind] 
## -0.0090857770  0.0005150538 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  103" "Indices =  104" "Indices =  105" "Indices =  106"
##  [5] "Indices =  107" "Indices =  108" "Indices =  109" "Indices =  110"
##  [9] "Indices =  111" "Indices =  112" "Indices =  113" "Indices =  114"
## [13] "Indices =  115" "Indices =  116" "Indices =  117"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0"           "Concs = 0"           "Concs = 0"          
## [10] "Concs = 0"           "Concs = 0.08814803"  "Concs = 0"          
## [13] "Concs = 0.636612173" "Concs = 0.308057976" "Concs = 0.343301822"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
## 
## Coefficients:
##  (Intercept)    Time[ind] 
## -0.060061083  0.003574623 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.089 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.154416 -0.047178  0.006442  0.060061  0.374957 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) -0.0601  0.0395    -1.5207
## Time[ind]    0.0036  0.0008     4.5837
## 
## Residual standard error: 0.08905 on 13 degrees of freedom

##  (Intercept)    Time[ind] 
## -0.060061083  0.003574623 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  118" "Indices =  119" "Indices =  120" "Indices =  121"
##  [5] "Indices =  122" "Indices =  123" "Indices =  124" "Indices =  125"
##  [9] "Indices =  126" "Indices =  127" "Indices =  128" "Indices =  129"
## [13] "Indices =  130"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.303186347" "Concs = 0.314346484" "Concs = 0.32890249" 
##  [7] "Concs = 0.470955087" "Concs = 0.418661875" "Concs = 0.69686814" 
## [10] "Concs = 0.65732937"  "Concs = 1.058297138" "Concs = 1.054151944"
## [13] "Concs = 0.826804017"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.08439208  0.01021475 
## 
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.114 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.17692 -0.08439  0.02783  0.06557  0.09129 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.0844  0.0383     2.2006
## Time[ind]    0.0102  0.0008    13.6170
## 
## Residual standard error: 0.1138 on 11 degrees of freedom

## (Intercept)   Time[ind] 
##  0.08439208  0.01021475 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  131" "Indices =  132" "Indices =  133" "Indices =  134"
##  [5] "Indices =  135" "Indices =  136" "Indices =  137" "Indices =  138"
##  [9] "Indices =  139" "Indices =  140" "Indices =  141" "Indices =  142"
## [13] "Indices =  143" "Indices =  144" "Indices =  145" "Indices =  146"
## [17] "Indices =  147" "Indices =  148"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15"
##  [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0.651134538" "Concs = 0.410418033"
##  [7] "Concs = 0.72633168"  "Concs = 0.655344167" "Concs = 1.213331632"
## [10] "Concs = 0.938854783" "Concs = 1.336588359" "Concs = 1.220393789"
## [13] "Concs = 2.258618197" "Concs = 2.185187246" "Concs = 2.037689206"
## [16] "Concs = 2.794152863" "Concs = 2.97663412"  "Concs = 2.702787847"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.11936774  0.03168274 
## 
## Degrees of freedom: 18 total; 16 residual
## Scale estimate: 0.195 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.26803 -0.11937  0.01159  0.14054  0.26674 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.1194  0.0661     1.8051
## Time[ind]    0.0317  0.0014    22.4729
## 
## Residual standard error: 0.1947 on 16 degrees of freedom

## (Intercept)   Time[ind] 
##  0.11936774  0.03168274 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## 'data.frame':    10 obs. of  2 variables:
##  $ sub: num  50 10 100 75 125 ...
##  $ vel: num  48.3 23.2 127.1 64.8 112.3 ...
##         sub        vel
## 1   50.0000  48.289594
## 2   10.0000  23.179265
## 3  100.0000 127.084516
## 4   75.0000  64.789315
## 5  125.0000 112.347269
## 6    0.7120   0.000000
## 7    3.1684   2.575269
## 8  200.0000  17.873113
## 9  250.0000  51.073730
## 10 150.0000 158.413706

## 
## Model fitted: Michaelis-Menten (2 parms)
## 
## Parameter estimates:
## 
##               Estimate Std. Error  t-value p-value
## d:(Intercept) 97.64281   29.77021  3.27988  0.0112
## e:(Intercept) 21.13369   29.70447  0.71146  0.4970
## 
## Residual standard error:
## 
##  44.01437 (8 degrees of freedom)

We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.

We are fitting the 2-parameter model.

Used to estimate slopes.

dia

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.17588934"  "Concs = 0.162027282" "Concs = 0.163356559"
##  [7] "Concs = 0.343213005" "Concs = 0.307927387" "Concs = 0.309459105"
## [10] "Concs = 0.560097677" "Concs = 0.54821645"  "Concs = 0.533109282"
## [13] "Concs = 0.73827321"  "Concs = 0.728694143" "Concs = 0.726811372"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 3 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 0.039703425 0.008028213 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0429 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.03970 -0.03449  0.00323  0.02710  0.06266 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.0397  0.0150     2.6499
## Time[ind]    0.0080  0.0003    27.1369
## 
## Residual standard error: 0.04286 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 0.039703425 0.008028213 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.037225886" "Concs = 0.038369499" "Concs = 0.046312162"
##  [7] "Concs = 0.08490015"  "Concs = 0.083838648" "Concs = 0.093345378"
## [10] "Concs = 0.209721193" "Concs = 0.168743119" "Concs = 0.161851994"
## [13] "Concs = 0.162150446" "Concs = 0.222852555" "Concs = 0.229604672"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 14 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 0.003164745 0.002624622 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0056 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.016528 -0.003665  0.001210  0.003387  0.049079 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.0032  0.0036     0.8757
## Time[ind]    0.0026  0.0001    34.5621
## 
## Residual standard error: 0.005601 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 0.003164745 0.002624622 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.519984026" "Concs = 0.456185794" "Concs = 0.465640368"
##  [7] "Concs = 0.969762496" "Concs = 0.925948373" "Concs = 0.828633383"
## [10] "Concs = 1.646101156" "Concs = 1.493978674" "Concs = 1.273473826"
## [13] "Concs = 2.097846916" "Concs = 1.845660879" "Concs = 1.775884862"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.14326104  0.02076955 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.212 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.23664 -0.14326  0.01084  0.09494  0.25667 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.1433  0.0633     2.2631
## Time[ind]    0.0208  0.0012    16.6170
## 
## Residual standard error: 0.2124 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  0.14326104  0.02076955 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59" "Indices =  60"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.105167732" "Concs = 0.164272494" "Concs = 0.177858813"
##  [7] "Concs = 0.289730134" "Concs = 0.302066953" "Concs = 0.387892352"
## [10] "Concs = 0.703975509" "Concs = 0.8027739"   "Concs = 0.718751156"
## [13] "Concs = 0.974859321" "Concs = 1.104369407" "Concs = 0.769135715"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
## 
## Coefficients:
##  (Intercept)    Time[ind] 
## -0.008202928  0.011576043 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0549 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.264505 -0.043180  0.008203  0.025004  0.116414 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) -0.0082  0.0233    -0.3526
## Time[ind]    0.0116  0.0005    25.2030
## 
## Residual standard error: 0.05487 on 13 degrees of freedom

##  (Intercept)    Time[ind] 
## -0.008202928  0.011576043 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  61" "Indices =  62" "Indices =  63" "Indices =  64"
##  [5] "Indices =  65" "Indices =  66" "Indices =  67" "Indices =  68"
##  [9] "Indices =  69" "Indices =  70" "Indices =  71" "Indices =  72"
## [13] "Indices =  73"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.558156141" "Concs = 0.453398653" "Concs = 0.457441572"
##  [7] "Concs = 0.819739976" "Concs = 0.818340148" "Concs = 1.39707951" 
## [10] "Concs = 1.483198815" "Concs = 1.818559552" "Concs = 1.850457042"
## [13] "Concs = 1.741234977"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##   0.1293156   0.0196293 
## 
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.151 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.15472 -0.12932  0.02964  0.10015  0.17613 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.1293  0.0504     2.5660
## Time[ind]    0.0196  0.0010    19.9121
## 
## Residual standard error: 0.1505 on 11 degrees of freedom

## (Intercept)   Time[ind] 
##   0.1293156   0.0196293 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  0.712"
##  [1] "Indices =  74" "Indices =  75" "Indices =  76" "Indices =  77"
##  [5] "Indices =  78" "Indices =  79" "Indices =  80" "Indices =  81"
##  [9] "Indices =  82" "Indices =  83" "Indices =  84" "Indices =  85"
## [13] "Indices =  86" "Indices =  87" "Indices =  88"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##  [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 0 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##           0           0 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##    Min     1Q Median     3Q    Max 
##      0      0      0      0      0 
## 
## Coefficients:
##             Value Std. Error t value
## (Intercept)   0   NaN        NaN    
## Time[ind]     0   NaN        NaN    
## 
## Residual standard error: 0 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##           0           0 
##             2.5 % 97.5 %
## (Intercept)   NaN    NaN
## Time[ind]     NaN    NaN
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  3.1684"
##  [1] "Indices =  89"  "Indices =  90"  "Indices =  91"  "Indices =  92" 
##  [5] "Indices =  93"  "Indices =  94"  "Indices =  95"  "Indices =  96" 
##  [9] "Indices =  97"  "Indices =  98"  "Indices =  99"  "Indices =  100"
## [13] "Indices =  101" "Indices =  102" "Indices =  103"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##  [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 0 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##           0           0 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##    Min     1Q Median     3Q    Max 
##      0      0      0      0      0 
## 
## Coefficients:
##             Value Std. Error t value
## (Intercept)   0   NaN        NaN    
## Time[ind]     0   NaN        NaN    
## 
## Residual standard error: 0 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##           0           0 
##             2.5 % 97.5 %
## (Intercept)   NaN    NaN
## Time[ind]     NaN    NaN
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  104" "Indices =  105" "Indices =  106" "Indices =  107"
##  [5] "Indices =  108" "Indices =  109" "Indices =  110" "Indices =  111"
##  [9] "Indices =  112" "Indices =  113" "Indices =  114" "Indices =  115"
## [13] "Indices =  116"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.488073154" "Concs = 0.494203709" "Concs = 0.58569046" 
##  [7] "Concs = 0.731173258" "Concs = 0.714667917" "Concs = 1.145221545"
## [10] "Concs = 1.154181588" "Concs = 1.638731263" "Concs = 1.563749853"
## [13] "Concs = 1.475092589"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 3 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##   0.1502412   0.0162300 
## 
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.14 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.15024 -0.13585  0.02779  0.09403  0.19200 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.1502  0.0550     2.7302
## Time[ind]    0.0162  0.0011    15.0778
## 
## Residual standard error: 0.1399 on 11 degrees of freedom

## (Intercept)   Time[ind] 
##   0.1502412   0.0162300 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  117" "Indices =  118" "Indices =  119" "Indices =  120"
##  [5] "Indices =  121" "Indices =  122" "Indices =  123" "Indices =  124"
##  [9] "Indices =  125" "Indices =  126" "Indices =  127" "Indices =  128"
## [13] "Indices =  129" "Indices =  130" "Indices =  131" "Indices =  132"
## [17] "Indices =  133" "Indices =  134"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15"
##  [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0.462309631" "Concs = 0.255700106"
##  [7] "Concs = 0.526463046" "Concs = 0.47230486"  "Concs = 0.931548447"
## [10] "Concs = 0.722337549" "Concs = 1.066740758" "Concs = 0.948249061"
## [13] "Concs = 1.827879364" "Concs = 1.789768545" "Concs = 1.614786398"
## [16] "Concs = 2.243971727" "Concs = 2.385364241" "Concs = 2.16439478" 
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.06159826  0.02581150 
## 
## Degrees of freedom: 18 total; 16 residual
## Scale estimate: 0.128 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.220238 -0.061598  0.002615  0.091127  0.230798 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.0616  0.0609     1.0121
## Time[ind]    0.0258  0.0013    19.8930
## 
## Residual standard error: 0.1285 on 16 degrees of freedom

## (Intercept)   Time[ind] 
##  0.06159826  0.02581150 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  135" "Indices =  136" "Indices =  137" "Indices =  138"
##  [5] "Indices =  139" "Indices =  140" "Indices =  141" "Indices =  142"
##  [9] "Indices =  143" "Indices =  144" "Indices =  145" "Indices =  146"
## [13] "Indices =  147" "Indices =  148" "Indices =  149"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0"           "Concs = 0"           "Concs = 0"          
## [10] "Concs = 0.147179292" "Concs = 0.49374336"  "Concs = 0.185151589"
## [13] "Concs = 0.905020781" "Concs = 0.751527127" "Concs = 0.778803003"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
##  (Intercept)    Time[ind] 
## -0.135091948  0.009038982 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.2 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.2600677 -0.1360775 -0.0004928  0.1177393  0.2266044 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) -0.1351  0.0616    -2.1918
## Time[ind]    0.0090  0.0012     7.4273
## 
## Residual standard error: 0.2003 on 13 degrees of freedom

##  (Intercept)    Time[ind] 
## -0.135091948  0.009038982 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## 'data.frame':    10 obs. of  2 variables:
##  $ sub: num  50 10 100 75 125 ...
##  $ vel: num  40.1 13.1 103.8 57.9 98.1 ...
##         sub       vel
## 1   50.0000  40.14107
## 2   10.0000  13.12311
## 3  100.0000 103.84774
## 4   75.0000  57.88021
## 5  125.0000  98.14650
## 6    0.7120   0.00000
## 7    3.1684   0.00000
## 8  250.0000  81.14999
## 9  150.0000 129.05748
## 10 200.0000  45.19491

## 
## Model fitted: Michaelis-Menten (2 parms)
## 
## Parameter estimates:
## 
##               Estimate Std. Error  t-value p-value
## d:(Intercept) 110.1071    29.6962   3.7078  0.0060
## e:(Intercept)  44.4716    40.7922   1.0902  0.3074
## 
## Residual standard error:
## 
##  26.75434 (8 degrees of freedom)

triadimefon

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.68082"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0.68082"     "Concs = 0.68082"     "Concs = 0.68082"    
##  [4] "Concs = 0.399443695" "Concs = 0.42224169"  "Concs = 0.36799564" 
##  [7] "Concs = 0.335043095" "Concs = 0.307545884" "Concs = 0.33049829" 
## [10] "Concs = 0.298781298" "Concs = 0.300851183" "Concs = 0.297372843"
## [13] "Concs = 0.30988245"  "Concs = 0.29724505"  "Concs = 0.293730776"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
##  (Intercept)    Time[ind] 
##  0.530169234 -0.003332387 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.12 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.12265 -0.08795 -0.03144  0.07331  0.15065 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.5302  0.0424    12.5176
## Time[ind]   -0.0033  0.0008    -3.9848
## 
## Residual standard error: 0.1197 on 13 degrees of freedom

##  (Intercept)    Time[ind] 
##  0.530169234 -0.003332387 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 10"          "Concs = 10"          "Concs = 10"         
##  [4] "Concs = 3.796829723" "Concs = 3.995422538" "Concs = 4.084402023"
##  [7] "Concs = 3.689670522" "Concs = 3.770627455" "Concs = 3.708045842"
## [10] "Concs = 2.923805377" "Concs = 2.81999575"  "Concs = 1.627429272"
## [13] "Concs = 1.556106647" "Concs = 1.615639352"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  7.24519589 -0.07208527 
## 
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 2.05 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.36709 -1.38837 -0.04818  0.86696  2.75480 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  7.2452  0.7850     9.2290
## Time[ind]   -0.0721  0.0157    -4.5830
## 
## Residual standard error: 2.052 on 12 degrees of freedom
## (Intercept)   Time[ind] 
##  7.24519589 -0.07208527 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  30" "Indices =  31" "Indices =  32" "Indices =  33"
##  [5] "Indices =  34" "Indices =  35" "Indices =  36" "Indices =  37"
##  [9] "Indices =  38" "Indices =  39" "Indices =  40" "Indices =  41"
## [13] "Indices =  42" "Indices =  43" "Indices =  44"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 2.89"        "Concs = 2.89"        "Concs = 2.89"       
##  [4] "Concs = 1.438977536" "Concs = 1.147878572" "Concs = 1.273836719"
##  [7] "Concs = 1.170628317" "Concs = 1.153347335" "Concs = 0.90609785" 
## [10] "Concs = 0.796555881" "Concs = 0.724314066" "Concs = 0.705525399"
## [13] "Concs = 0.684015583" "Concs = 0.645877009" "Concs = 0.633912406"
## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Ran 20 iterations without convergence
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  1.74179311 -0.01438885 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.296 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.40403 -0.16486 -0.08698  0.21815  1.14821 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  1.7418  0.1676    10.3908
## Time[ind]   -0.0144  0.0033    -4.3473
## 
## Residual standard error: 0.2961 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  1.74179311 -0.01438885 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  45" "Indices =  46" "Indices =  47" "Indices =  48"
##  [5] "Indices =  49" "Indices =  50" "Indices =  51" "Indices =  52"
##  [9] "Indices =  53" "Indices =  54" "Indices =  55" "Indices =  56"
## [13] "Indices =  57"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 50"          "Concs = 50"          "Concs = 50"         
##  [4] "Concs = 25.6223204"  "Concs = 24.15898057" "Concs = 24.97516518"
##  [7] "Concs = 26.62994332" "Concs = 26.25228145" "Concs = 25.95782864"
## [10] "Concs = 28.59868326" "Concs = 22.32352998" "Concs = 22.61126729"
## [13] "Concs = 22.93204565"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  38.6877394  -0.2078355 
## 
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 9.19 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -11.411  -6.200   2.341   2.950  11.312 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 38.6877  3.5986    10.7508
## Time[ind]   -0.2078  0.0704    -2.9525
## 
## Residual standard error: 9.193 on 11 degrees of freedom
## (Intercept)   Time[ind] 
##  38.6877394  -0.2078355 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  58" "Indices =  59" "Indices =  60" "Indices =  61"
##  [5] "Indices =  62" "Indices =  63" "Indices =  64" "Indices =  65"
##  [9] "Indices =  66" "Indices =  67" "Indices =  68" "Indices =  69"
## [13] "Indices =  70" "Indices =  71" "Indices =  72"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 75"          "Concs = 75"          "Concs = 75"         
##  [4] "Concs = 39.60290919" "Concs = 36.37647057" "Concs = 38.41537648"
##  [7] "Concs = 41.36228948" "Concs = 39.60347726" "Concs = 37.05197615"
## [10] "Concs = 38.79077057" "Concs = 39.14694989" "Concs = 38.88285882"
## [13] "Concs = 38.84162326" "Concs = 38.38496898" "Concs = 38.08875118"
## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Ran 20 iterations without convergence
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 43.56867863 -0.07261069 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 3.13 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -6.10305 -2.33174 -0.06509  1.57958 31.43132 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 43.5687  2.0022    21.7602
## Time[ind]   -0.0726  0.0395    -1.8367
## 
## Residual standard error: 3.132 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 43.56867863 -0.07261069 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  73" "Indices =  74" "Indices =  75" "Indices =  76"
##  [5] "Indices =  77" "Indices =  78" "Indices =  79" "Indices =  80"
##  [9] "Indices =  81" "Indices =  82" "Indices =  83" "Indices =  84"
## [13] "Indices =  85" "Indices =  86" "Indices =  87"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 100"         "Concs = 100"         "Concs = 100"        
##  [4] "Concs = 49.24893567" "Concs = 52.23999837" "Concs = 54.94800062"
##  [7] "Concs = 51.63283427" "Concs = 55.62979138" "Concs = 53.25296347"
## [10] "Concs = 57.2285182"  "Concs = 52.25557462" "Concs = 57.56142454"
## [13] "Concs = 55.15134637" "Concs = 52.80788424" "Concs = 54.77096052"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  75.7962700  -0.3251552 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 19 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -21.6700 -13.5987   0.9416   8.4289  24.2037 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 75.7963  6.6510    11.3963
## Time[ind]   -0.3252  0.1313    -2.4760
## 
## Residual standard error: 18.96 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  75.7962700  -0.3251552 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  88"  "Indices =  89"  "Indices =  90"  "Indices =  91" 
##  [5] "Indices =  92"  "Indices =  93"  "Indices =  94"  "Indices =  95" 
##  [9] "Indices =  96"  "Indices =  97"  "Indices =  98"  "Indices =  99" 
## [13] "Indices =  100" "Indices =  101"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 125"         "Concs = 125"         "Concs = 125"        
##  [4] "Concs = 54.97761564" "Concs = 64.19295623" "Concs = 61.97688614"
##  [7] "Concs = 68.89112849" "Concs = 56.33566744" "Concs = 71.31751913"
## [10] "Concs = 66.04862513" "Concs = 69.71262134" "Concs = 57.48171016"
## [13] "Concs = 60.79276739" "Concs = 57.42314849"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  94.1185302  -0.4828739 
## 
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 24.8 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -31.898 -19.697   2.735   9.305  30.881 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 94.1185  9.0233    10.4306
## Time[ind]   -0.4829  0.1808    -2.6709
## 
## Residual standard error: 24.78 on 12 degrees of freedom
## (Intercept)   Time[ind] 
##  94.1185302  -0.4828739 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  102" "Indices =  103" "Indices =  104" "Indices =  105"
##  [5] "Indices =  106" "Indices =  107" "Indices =  108" "Indices =  109"
##  [9] "Indices =  110" "Indices =  111" "Indices =  112" "Indices =  113"
## [13] "Indices =  114" "Indices =  115"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 15"
##  [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 150"         "Concs = 150"         "Concs = 78.63355587"
##  [4] "Concs = 62.93987056" "Concs = 106.7018113" "Concs = 73.37624336"
##  [7] "Concs = 66.9635187"  "Concs = 95.5133834"  "Concs = 69.7678651" 
## [10] "Concs = 58.53815945" "Concs = 61.06336245" "Concs = 82.43537943"
## [13] "Concs = 75.76324133" "Concs = 73.77914496"
## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Ran 20 iterations without convergence
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 101.3079410  -0.4215165 
## 
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 23.5 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -32.0453 -16.0853   0.3009  12.2230  48.6921 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept) 101.3079  12.3785     8.1842
## Time[ind]    -0.4215   0.2361    -1.7851
## 
## Residual standard error: 23.47 on 12 degrees of freedom

## (Intercept)   Time[ind] 
## 101.3079410  -0.4215165 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  116" "Indices =  117" "Indices =  118" "Indices =  119"
##  [5] "Indices =  120" "Indices =  121" "Indices =  122" "Indices =  123"
##  [9] "Indices =  124" "Indices =  125" "Indices =  126" "Indices =  127"
## [13] "Indices =  128" "Indices =  129" "Indices =  130"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 200"         "Concs = 200"         "Concs = 200"        
##  [4] "Concs = 338.7826757" "Concs = 357.9520843" "Concs = 202.0964578"
##  [7] "Concs = 422.3552358" "Concs = 340.5253492" "Concs = 345.8291382"
## [10] "Concs = 359.4674526" "Concs = 377.2730298" "Concs = 186.1093226"
## [13] "Concs = 471.6047045" "Concs = 376.1365036" "Concs = 190.6933116"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 9 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  255.779660    1.454499 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 82.7 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -195.99  -55.78   16.42   53.80  122.94 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept) 255.7797  39.7870     6.4287
## Time[ind]     1.4545   0.7856     1.8515
## 
## Residual standard error: 82.7 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  255.779660    1.454499 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  131" "Indices =  132" "Indices =  133" "Indices =  134"
##  [5] "Indices =  135" "Indices =  136" "Indices =  137" "Indices =  138"
##  [9] "Indices =  139" "Indices =  140" "Indices =  141" "Indices =  142"
## [13] "Indices =  143" "Indices =  144"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 15"
##  [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 250"         "Concs = 250"         "Concs = 186.8824662"
##  [4] "Concs = 208.9457498" "Concs = 167.0779465" "Concs = 229.5166359"
##  [7] "Concs = 99.11335239" "Concs = 263.0350796" "Concs = 59.52448054"
## [10] "Concs = 46.29054385" "Concs = 51.98182232" "Concs = 162.0360626"
## [13] "Concs = 200.5560551" "Concs = 187.8908429"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 209.0664272  -0.9642375 
## 
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 85.2 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -104.92  -67.65   27.05   47.27   82.90 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept) 209.0664  31.6894     6.5974
## Time[ind]    -0.9642   0.6045    -1.5951
## 
## Residual standard error: 85.24 on 12 degrees of freedom

## (Intercept)   Time[ind] 
## 209.0664272  -0.9642375 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## 'data.frame':    10 obs. of  2 variables:
##  $ sub: num  0.681 10 2.89 50 75 ...
##  $ vel: num  -16.7 -360.4 -71.9 -1039.2 -363.1 ...
##          sub         vel
## 1    0.68082   -16.66194
## 2   10.00000  -360.42636
## 3    2.89000   -71.94424
## 4   50.00000 -1039.17744
## 5   75.00000  -363.05343
## 6  100.00000 -1625.77622
## 7  125.00000 -2414.36930
## 8  150.00000 -2107.58237
## 9  200.00000  7272.49406
## 10 250.00000 -4821.18755

## 
## Model fitted: Michaelis-Menten (2 parms)
## 
## Parameter estimates:
## 
##                 Estimate Std. Error    t-value p-value
## d:(Intercept) -745.65932 1444.04137   -0.51637  0.6196
## e:(Intercept)    6.46479   70.23134    0.09205  0.9289
## 
## Residual standard error:
## 
##  3291.458 (8 degrees of freedom)

tdla

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.68"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.124349504" "Concs = 0.14627783"  "Concs = 0.089752887"
##  [7] "Concs = 0.107638677" "Concs = 0.159434476" "Concs = 0.159787554"
## [10] "Concs = 0.099828091" "Concs = 0.225228369" "Concs = 0.139329405"
## [13] "Concs = 0.072482112" "Concs = 0.09994686"  "Concs = 0.061506341"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
##  (Intercept)    Time[ind] 
## 0.0761456879 0.0005869689 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0909 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.076146 -0.061979  0.004803  0.050363  0.113865 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 0.0761 0.0261     2.9175 
## Time[ind]   0.0006 0.0005     1.1390 
## 
## Residual standard error: 0.09092 on 13 degrees of freedom

##  (Intercept)    Time[ind] 
## 0.0761456879 0.0005869689 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.562008549" "Concs = 0.514503123" "Concs = 0.553400833"
##  [7] "Concs = 0.914781067" "Concs = 0.896944628" "Concs = 0.854682343"
## [10] "Concs = 0.640465968" "Concs = 1.46510307"  "Concs = 1.529173181"
## [13] "Concs = 1.670981262" "Concs = 1.594325825" "Concs = 1.598291535"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.20550710  0.01697908 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.27 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.58379 -0.17240  0.05431  0.16093  0.30492 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 0.2055 0.0914     2.2488 
## Time[ind]   0.0170 0.0018     9.4097 
## 
## Residual standard error: 0.2699 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  0.20550710  0.01697908 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.587769932" "Concs = 0.500911907" "Concs = 2.390614252"
##  [7] "Concs = 0.732569141" "Concs = 0.819349521" "Concs = 0.882196657"
## [10] "Concs = 1.272480799" "Concs = 1.332879865" "Concs = 1.171215513"
## [13] "Concs = 1.284978616" "Concs = 1.466507839"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.24636291  0.01492835 
## 
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.236 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.30494 -0.21562  0.03449  0.12910  1.92033 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 0.2464 0.0925     2.6647 
## Time[ind]   0.0149 0.0020     7.5210 
## 
## Residual standard error: 0.236 on 12 degrees of freedom

## (Intercept)   Time[ind] 
##  0.24636291  0.01492835 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  45" "Indices =  46" "Indices =  47" "Indices =  48"
##  [5] "Indices =  49" "Indices =  50" "Indices =  51" "Indices =  52"
##  [9] "Indices =  53" "Indices =  54" "Indices =  55" "Indices =  56"
## [13] "Indices =  57" "Indices =  58" "Indices =  59"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.366202494" "Concs = 2.316676352" "Concs = 2.98040696" 
##  [7] "Concs = 2.746818134" "Concs = 3.431666105" "Concs = 3.294563534"
## [10] "Concs = 3.820882667" "Concs = 4.627112685" "Concs = 4.219456142"
## [13] "Concs = 4.7035697"   "Concs = 4.419483485" "Concs = 4.677842802"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  1.16197557  0.04474367 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.14 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1620 -0.6402  0.2425  0.6568  1.1473 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 1.1620 0.3417     3.4008 
## Time[ind]   0.0447 0.0067     6.6322 
## 
## Residual standard error: 1.141 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  1.16197557  0.04474367 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  60" "Indices =  61" "Indices =  62" "Indices =  63"
##  [5] "Indices =  64" "Indices =  65" "Indices =  66" "Indices =  67"
##  [9] "Indices =  68" "Indices =  69" "Indices =  70" "Indices =  71"
## [13] "Indices =  72" "Indices =  73" "Indices =  74"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.219185884" "Concs = 2.155328801" "Concs = 2.202708256"
##  [7] "Concs = 2.811019032" "Concs = 2.229132105" "Concs = 2.319209877"
## [10] "Concs = 3.438186485" "Concs = 3.239731804" "Concs = 3.112249253"
## [13] "Concs = 3.973569475" "Concs = 3.922150065" "Concs = 3.990347195"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 14 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  1.30612603  0.03145706 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.363 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.30613 -0.18940 -0.02071  0.31099  0.56118 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 1.3061 0.2061     6.3384 
## Time[ind]   0.0315 0.0041     7.7313 
## 
## Residual standard error: 0.3627 on 13 degrees of freedom
## (Intercept)   Time[ind] 
##  1.30612603  0.03145706 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  75" "Indices =  76" "Indices =  77" "Indices =  78"
##  [5] "Indices =  79" "Indices =  80" "Indices =  81" "Indices =  82"
##  [9] "Indices =  83" "Indices =  84" "Indices =  85" "Indices =  86"
## [13] "Indices =  87" "Indices =  88" "Indices =  89"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.973173898" "Concs = 4.278761105" "Concs = 5.203600328"
##  [7] "Concs = 3.752087918" "Concs = 4.489689601" "Concs = 4.3820044"  
## [10] "Concs = 4.18858056"  "Concs = 4.787062374" "Concs = 4.819935077"
## [13] "Concs = 5.229225315" "Concs = 5.541134166" "Concs = 5.363637277"
## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Ran 20 iterations without convergence
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  2.52347511  0.03490097 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.646 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.52348 -0.43214 -0.07382  0.50695  2.15661 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 2.5235 0.4925     5.1243 
## Time[ind]   0.0349 0.0097     3.5893 
## 
## Residual standard error: 0.6461 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  2.52347511  0.03490097 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  90"  "Indices =  91"  "Indices =  92"  "Indices =  93" 
##  [5] "Indices =  94"  "Indices =  95"  "Indices =  96"  "Indices =  97" 
##  [9] "Indices =  98"  "Indices =  99"  "Indices =  100" "Indices =  101"
## [13] "Indices =  102" "Indices =  103" "Indices =  104"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 3.664975002" "Concs = 5.128116042" "Concs = 3.342678541"
##  [7] "Concs = 3.909877303" "Concs = 3.131834777" "Concs = 6.184369077"
## [10] "Concs = 5.034115174" "Concs = 6.997125798" "Concs = 5.513028895"
## [13] "Concs = 5.609126979" "Concs = 6.565737598" "Concs = 6.051117386"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##   1.7560769   0.0576901 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.55 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7561 -1.1181 -0.1834  0.8824  2.6976 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 1.7561 0.6731     2.6090 
## Time[ind]   0.0577 0.0133     4.3408 
## 
## Residual standard error: 1.547 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##   1.7560769   0.0576901 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  105" "Indices =  106" "Indices =  107" "Indices =  108"
##  [5] "Indices =  109" "Indices =  110" "Indices =  111" "Indices =  112"
##  [9] "Indices =  113" "Indices =  114" "Indices =  115" "Indices =  116"
## [13] "Indices =  117" "Indices =  118" "Indices =  119"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 4.690841414" "Concs = 4.417155339" "Concs = 6.21277087" 
##  [7] "Concs = 3.839544319" "Concs = 4.519625245" "Concs = 6.760429619"
## [10] "Concs = 7.2240805"   "Concs = 3.468203577" "Concs = 4.462789205"
## [13] "Concs = 8.035064896" "Concs = 8.748204845" "Concs = 7.504701282"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  2.03606128  0.06725212 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 2.38 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.60299 -1.82223 -0.05369  1.26260  3.16793 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 2.0361 0.7623     2.6708 
## Time[ind]   0.0673 0.0151     4.4679 
## 
## Residual standard error: 2.385 on 13 degrees of freedom
## (Intercept)   Time[ind] 
##  2.03606128  0.06725212 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  120" "Indices =  121" "Indices =  122" "Indices =  123"
##  [5] "Indices =  124" "Indices =  125" "Indices =  126" "Indices =  127"
##  [9] "Indices =  128" "Indices =  129" "Indices =  130"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 30"
##  [6] "Times = 30" "Times = 60" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 17.81066063"
##  [4] "Concs = 14.08273374" "Concs = 20.76679639" "Concs = 16.9957259" 
##  [7] "Concs = 18.08230553" "Concs = 16.51635254" "Concs = 17.9065353" 
## [10] "Concs = 19.61630031" "Concs = 17.39520371"
## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Ran 20 iterations without convergence
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  10.8512483   0.1088307 
## 
## Degrees of freedom: 11 total; 9 residual
## Scale estimate: 4.31 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.8512  -2.1403   0.5254   2.2393   6.6506 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 10.8512  3.0214     3.5914
## Time[ind]    0.1088  0.0586     1.8574
## 
## Residual standard error: 4.313 on 9 degrees of freedom

## (Intercept)   Time[ind] 
##  10.8512483   0.1088307 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  0.68 10 2.89 50 75 100 125 150 250
##  $ vel: num  2.93 84.9 74.64 223.72 157.29 ...
##      sub        vel
## 1   0.68   2.934844
## 2  10.00  84.895393
## 3   2.89  74.641768
## 4  50.00 223.718355
## 5  75.00 157.285301
## 6 100.00 174.504835
## 7 125.00 288.450483
## 8 150.00 336.260615
## 9 250.00 544.153446

## 
## Model fitted: Michaelis-Menten (2 parms)
## 
## Parameter estimates:
## 
##                 Estimate Std. Error    t-value p-value
## d:(Intercept) 3163.18381 4980.22485    0.63515  0.5455
## e:(Intercept) 1238.39731 2229.91648    0.55536  0.5959
## 
## Residual standard error:
## 
##  57.11426 (7 degrees of freedom)

tdlb

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  0.68"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.159849035" "Concs = 0.171671782" "Concs = 0.137258352"
##  [7] "Concs = 0.135498718" "Concs = 0.166579942" "Concs = 0.160555121"
## [10] "Concs = 0.085155894" "Concs = 0.137641779" "Concs = 0.101223849"
## [13] "Concs = 0.041122976" "Concs = 0.056120989" "Concs = 0.040770384"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 11 iterations
## 
## Coefficients:
##   (Intercept)     Time[ind] 
##  0.1007351193 -0.0001600198 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.069 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.10074 -0.04539  0.01009  0.05401  0.07334 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.1007  0.0339     2.9681
## Time[ind]   -0.0002  0.0007    -0.2388
## 
## Residual standard error: 0.06895 on 13 degrees of freedom

##   (Intercept)     Time[ind] 
##  0.1007351193 -0.0001600198 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.540578005" "Concs = 0.535327972" "Concs = 0.549947891"
##  [7] "Concs = 0.963906807" "Concs = 0.939249694" "Concs = 0.8832653"  
## [10] "Concs = 0.462660817" "Concs = 1.424227752" "Concs = 1.466547242"
## [13] "Concs = 1.470094516" "Concs = 1.424845158" "Concs = 1.471282702"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 3 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.24121948  0.01487844 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.358 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.67126 -0.19833  0.07093  0.22368  0.33262 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 0.2412 0.1117     2.1597 
## Time[ind]   0.0149 0.0022     6.7465 
## 
## Residual standard error: 0.3576 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  0.24121948  0.01487844 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.502687773" "Concs = 0.443748362" "Concs = 1.739413295"
##  [7] "Concs = 0.631006803" "Concs = 0.676925019" "Concs = 0.712219102"
## [10] "Concs = 0.887492395" "Concs = 0.922424215" "Concs = 0.774293903"
## [13] "Concs = 0.733501521" "Concs = 0.837366651" "Concs = 0.76078022" 
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 0.294045960 0.007259556 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.277 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.29405 -0.20027  0.04467  0.16148  1.33647 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 0.2940 0.0978     3.0069 
## Time[ind]   0.0073 0.0019     3.7597 
## 
## Residual standard error: 0.2767 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 0.294045960 0.007259556 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59" "Indices =  60"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.598887073" "Concs = 2.355603277" "Concs = 3.141649164"
##  [7] "Concs = 3.674320887" "Concs = 4.289723095" "Concs = 4.280136564"
## [10] "Concs = 6.243599629" "Concs = 6.734010485" "Concs = 6.361017452"
## [13] "Concs = 7.195467955" "Concs = 6.834134189" "Concs = 6.9532999"  
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  1.12601129  0.07482339 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.34 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1260 -0.9664  0.3036  0.8194  1.1186 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  1.1260  0.3726     3.0221
## Time[ind]    0.0748  0.0074    10.1706
## 
## Residual standard error: 1.344 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  1.12601129  0.07482339 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  61" "Indices =  62" "Indices =  63" "Indices =  64"
##  [5] "Indices =  65" "Indices =  66" "Indices =  67" "Indices =  68"
##  [9] "Indices =  69" "Indices =  70" "Indices =  71" "Indices =  72"
## [13] "Indices =  73" "Indices =  74" "Indices =  75"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.526757358" "Concs = 2.313637237" "Concs = 2.49086012" 
##  [7] "Concs = 3.789628052" "Concs = 3.174642429" "Concs = 3.191438558"
## [10] "Concs = 5.432233942" "Concs = 4.969157891" "Concs = 5.064503301"
## [13] "Concs = 6.712664257" "Concs = 6.597464296" "Concs = 6.484914"   
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.85929819  0.06813407 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.719 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8593 -0.4502  0.1172  0.4586  0.8863 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.8593  0.2477     3.4686
## Time[ind]    0.0681  0.0049    13.9290
## 
## Residual standard error: 0.7189 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  0.85929819  0.06813407 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  76" "Indices =  77" "Indices =  78" "Indices =  79"
##  [5] "Indices =  80" "Indices =  81" "Indices =  82" "Indices =  83"
##  [9] "Indices =  84" "Indices =  85" "Indices =  86" "Indices =  87"
## [13] "Indices =  88" "Indices =  89" "Indices =  90"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.987986855" "Concs = 4.62322369"  "Concs = 5.738654903"
##  [7] "Concs = 5.010985215" "Concs = 6.920302664" "Concs = 6.308852644"
## [10] "Concs = 8.11715413"  "Concs = 8.804687457" "Concs = 8.950282552"
## [13] "Concs = 10.81651263" "Concs = 11.45788264" "Concs = 11.01782631"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##   1.6091805   0.1129751 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.42 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.6092 -0.8598 -0.2705  0.9365  2.4348 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 1.6092 0.6040     2.6640 
## Time[ind]   0.1130 0.0119     9.4723 
## 
## Residual standard error: 1.424 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##   1.6091805   0.1129751 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  91"  "Indices =  92"  "Indices =  93"  "Indices =  94" 
##  [5] "Indices =  95"  "Indices =  96"  "Indices =  97"  "Indices =  98" 
##  [9] "Indices =  99"  "Indices =  100" "Indices =  101" "Indices =  102"
## [13] "Indices =  103" "Indices =  104" "Indices =  105"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 4.759629498" "Concs = 6.081131385" "Concs = 4.761075887"
##  [7] "Concs = 6.970865526" "Concs = 5.864292522" "Concs = 8.990170569"
## [10] "Concs = 10.29254833" "Concs = 11.89986315" "Concs = 10.55439287"
## [13] "Concs = 12.66145718" "Concs = 13.84087365" "Concs = 12.77355717"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 3 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##   2.0103474   0.1354138 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 2.11 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0103 -1.4801  0.1574  0.8088  2.9174 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 2.0103 0.7091     2.8353 
## Time[ind]   0.1354 0.0140     9.6723 
## 
## Residual standard error: 2.111 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##   2.0103474   0.1354138 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  106" "Indices =  107" "Indices =  108" "Indices =  109"
##  [5] "Indices =  110" "Indices =  111" "Indices =  112" "Indices =  113"
##  [9] "Indices =  114" "Indices =  115" "Indices =  116" "Indices =  117"
## [13] "Indices =  118" "Indices =  119" "Indices =  120"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 6.090475637" "Concs = 5.80525893"  "Concs = 8.98551562" 
##  [7] "Concs = 6.941039356" "Concs = 7.206821805" "Concs = 10.94796175"
## [10] "Concs = 13.80091931" "Concs = 7.457397291" "Concs = 9.668427529"
## [13] "Concs = 16.81467648" "Concs = 18.96446187" "Concs = 16.539466"  
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##   2.0306945   0.1686676 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 2.6 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.6934 -2.0307 -0.1497  1.5900  4.4248 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 2.0307 1.1765     1.7260 
## Time[ind]   0.1687 0.0232     7.2605 
## 
## Residual standard error: 2.6 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##   2.0306945   0.1686676 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  121" "Indices =  122" "Indices =  123" "Indices =  124"
##  [5] "Indices =  125" "Indices =  126" "Indices =  127" "Indices =  128"
##  [9] "Indices =  129" "Indices =  130" "Indices =  131"
##  [1] "Times = 0"  "Times = 0"  "Times = 15" "Times = 15" "Times = 30"
##  [6] "Times = 30" "Times = 60" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 22.19280552"
##  [4] "Concs = 17.62020275" "Concs = 24.15778887" "Concs = 20.49970666"
##  [7] "Concs = 25.33183553" "Concs = 23.63873667" "Concs = 25.85088774"
## [10] "Concs = 28.34728168" "Concs = 25.77673742"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 18 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  14.9606591   0.1539254 
## 
## Degrees of freedom: 11 total; 9 residual
## Scale estimate: 2.45 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.9607  -1.7973   0.3507   1.3952   4.9233 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 14.9607  2.2073     6.7778
## Time[ind]    0.1539  0.0428     3.5960
## 
## Residual standard error: 2.453 on 9 degrees of freedom

## (Intercept)   Time[ind] 
##  14.9606591   0.1539254 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  0.68 10 2.89 50 75 100 125 150 250
##  $ vel: num  -0.8 74.4 36.3 374.1 340.7 ...
##      sub         vel
## 1   0.68  -0.8000989
## 2  10.00  74.3921896
## 3   2.89  36.2977812
## 4  50.00 374.1169252
## 5  75.00 340.6703300
## 6 100.00 564.8754297
## 7 125.00 677.0688071
## 8 150.00 843.3378548
## 9 250.00 769.6270565

## 
## Model fitted: Michaelis-Menten (2 parms)
## 
## Parameter estimates:
## 
##                Estimate Std. Error   t-value p-value
## d:(Intercept) 1299.5681   282.4222    4.6015  0.0025
## e:(Intercept)  130.7062    57.0056    2.2929  0.0556
## 
## Residual standard error:
## 
##  83.93925 (7 degrees of freedom)

fipronil

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 10"          "Concs = 10"          "Concs = 10"         
##  [4] "Concs = 7.601993848" "Concs = 11.87171779" "Concs = 8.347482218"
##  [7] "Concs = 12.54233702" "Concs = 9.213313367" "Concs = 10.38856477"
## [10] "Concs = 12.36949156" "Concs = 8.215365646" "Concs = 11.17931895"
## [13] "Concs = 12.71923746" "Concs = 9.99477721" 
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##   9.7136033   0.0148301 
## 
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 2.02 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3880 -1.0264  0.2087  1.3248  2.3838 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  9.7136  0.6968    13.9394
## Time[ind]    0.0148  0.0133     1.1124
## 
## Residual standard error: 2.02 on 12 degrees of freedom

## (Intercept)   Time[ind] 
##   9.7136033   0.0148301 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  15" "Indices =  16" "Indices =  17" "Indices =  18"
##  [5] "Indices =  19" "Indices =  20" "Indices =  21" "Indices =  22"
##  [9] "Indices =  23" "Indices =  24" "Indices =  25" "Indices =  26"
## [13] "Indices =  27" "Indices =  28" "Indices =  29"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 2.89"        "Concs = 2.89"        "Concs = 2.89"       
##  [4] "Concs = 0.961731316" "Concs = 0.608701865" "Concs = 2.021395291"
##  [7] "Concs = 0.34095865"  "Concs = 1.416552854" "Concs = 4.678731136"
## [10] "Concs = 1.597568113" "Concs = 2.059112975" "Concs = 4.336224939"
## [13] "Concs = 0.73593197"  "Concs = 1.01143428"  "Concs = 2.098949857"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
## 
## Coefficients:
##  (Intercept)    Time[ind] 
##  2.239880567 -0.009035236 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.964 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.62786 -0.62152 -0.08296  0.65012  2.70991 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  2.2399  0.5303     4.2238
## Time[ind]   -0.0090  0.0105    -0.8629
## 
## Residual standard error: 0.9636 on 13 degrees of freedom

##  (Intercept)    Time[ind] 
##  2.239880567 -0.009035236 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  30" "Indices =  31" "Indices =  32" "Indices =  33"
##  [5] "Indices =  34" "Indices =  35" "Indices =  36" "Indices =  37"
##  [9] "Indices =  38" "Indices =  39" "Indices =  40" "Indices =  41"
## [13] "Indices =  42" "Indices =  43" "Indices =  44"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 50"          "Concs = 50"          "Concs = 50"         
##  [4] "Concs = 223.3849191" "Concs = 19.09530124" "Concs = 61.85004879"
##  [7] "Concs = 76.72890033" "Concs = 65.4447593"  "Concs = 59.88633813"
## [10] "Concs = 74.09066447" "Concs = 65.54242812" "Concs = 39.55208359"
## [13] "Concs = 66.15498564" "Concs = 23.55175796" "Concs = 58.25965938"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 10 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 56.75972024  0.05173236 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 10 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -38.440  -6.760   1.575   6.406 165.849 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 56.7597  7.5676     7.5003
## Time[ind]    0.0517  0.1494     0.3462
## 
## Residual standard error: 10.02 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 56.75972024  0.05173236 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  45" "Indices =  46" "Indices =  47" "Indices =  48"
##  [5] "Indices =  49" "Indices =  50" "Indices =  51" "Indices =  52"
##  [9] "Indices =  53" "Indices =  54" "Indices =  55" "Indices =  56"
## [13] "Indices =  57" "Indices =  58"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 75"          "Concs = 75"          "Concs = 75"         
##  [4] "Concs = 35.05455395" "Concs = 40.30349338" "Concs = 44.1381674" 
##  [7] "Concs = 38.08049817" "Concs = 38.34527612" "Concs = 89.31881211"
## [10] "Concs = 40.27279664" "Concs = 55.95173867" "Concs = 37.82415225"
## [13] "Concs = 32.32010713" "Concs = 45.93427684"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  61.0033064  -0.2664754 
## 
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 20.8 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -21.952 -14.215  -1.948  13.232  36.310 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 61.0033  6.9492     8.7785
## Time[ind]   -0.2665  0.1392    -1.9139
## 
## Residual standard error: 20.75 on 12 degrees of freedom

## (Intercept)   Time[ind] 
##  61.0033064  -0.2664754 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  59" "Indices =  60" "Indices =  61" "Indices =  62"
##  [5] "Indices =  63" "Indices =  64" "Indices =  65" "Indices =  66"
##  [9] "Indices =  67" "Indices =  68" "Indices =  69" "Indices =  70"
## [13] "Indices =  71" "Indices =  72" "Indices =  73"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 100"         "Concs = 100"         "Concs = 100"        
##  [4] "Concs = 65.75118371" "Concs = 61.03836189" "Concs = 86.42270417"
##  [7] "Concs = 18.77293974" "Concs = 84.04356305" "Concs = 89.30314297"
## [10] "Concs = 60.95565287" "Concs = 89.79580177" "Concs = 90.59062961"
## [13] "Concs = 56.03613412" "Concs = 94.58659729" "Concs = 89.70085579"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 85.20373140 -0.09753929 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 21.9 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -63.505 -18.193   7.026  14.036  18.161 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 85.2037  7.6083    11.1988
## Time[ind]   -0.0975  0.1502    -0.6493
## 
## Residual standard error: 21.94 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 85.20373140 -0.09753929 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  74" "Indices =  75" "Indices =  76" "Indices =  77"
##  [5] "Indices =  78" "Indices =  79" "Indices =  80" "Indices =  81"
##  [9] "Indices =  82" "Indices =  83" "Indices =  84" "Indices =  85"
## [13] "Indices =  86" "Indices =  87" "Indices =  88"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 125"         "Concs = 125"         "Concs = 125"        
##  [4] "Concs = 62.24891641" "Concs = 54.68420677" "Concs = 91.10795719"
##  [7] "Concs = 51.66702524" "Concs = 65.6950903"  "Concs = 112.1237445"
## [10] "Concs = 62.81350539" "Concs = 74.14828799" "Concs = 93.87631612"
## [13] "Concs = 59.80299767" "Concs = 82.33654045" "Concs = 89.20514072"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##   97.525349   -0.321659 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 32.9 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -38.016 -18.796  -1.593  22.439  27.475 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) 97.5253 10.1778     9.5821
## Time[ind]   -0.3217  0.2010    -1.6006
## 
## Residual standard error: 32.88 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##   97.525349   -0.321659 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  89"  "Indices =  90"  "Indices =  91"  "Indices =  92" 
##  [5] "Indices =  93"  "Indices =  94"  "Indices =  95"  "Indices =  96" 
##  [9] "Indices =  97"  "Indices =  98"  "Indices =  99"  "Indices =  100"
## [13] "Indices =  101" "Indices =  102" "Indices =  103"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 150"         "Concs = 150"         "Concs = 150"        
##  [4] "Concs = 37.15191594" "Concs = 76.95257401" "Concs = 82.83018255"
##  [7] "Concs = 89.28298886" "Concs = 103.9076465" "Concs = 88.89209516"
## [10] "Concs = 75.20034761" "Concs = 99.21349783" "Concs = 86.10641447"
## [13] "Concs = 85.35534061" "Concs = 86.89358929" "Concs = 19.45762438"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 118.4201583  -0.6413674 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 38.5 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -71.648 -18.128   4.729  25.427  31.580 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept) 118.4202  12.7515     9.2868
## Time[ind]    -0.6414   0.2518    -2.5474
## 
## Residual standard error: 38.51 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 118.4201583  -0.6413674 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  104" "Indices =  105" "Indices =  106" "Indices =  107"
##  [5] "Indices =  108" "Indices =  109" "Indices =  110" "Indices =  111"
##  [9] "Indices =  112" "Indices =  113" "Indices =  114" "Indices =  115"
## [13] "Indices =  116" "Indices =  117" "Indices =  118"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 200"         "Concs = 200"         "Concs = 200"        
##  [4] "Concs = 143.5820327" "Concs = 117.0381728" "Concs = 105.3992543"
##  [7] "Concs = 120.601107"  "Concs = 115.1379412" "Concs = 126.1830373"
## [10] "Concs = 91.91948648" "Concs = 106.6462813" "Concs = 72.50149496"
## [13] "Concs = 112.4063583" "Concs = 105.3992543" "Concs = 111.7531537"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 160.8018480  -0.8264276 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 37.6 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -43.006 -20.084  -4.823  25.656  39.198 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept) 160.8018  12.1956    13.1853
## Time[ind]    -0.8264   0.2408    -3.4320
## 
## Residual standard error: 37.55 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 160.8018480  -0.8264276 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  119" "Indices =  120" "Indices =  121" "Indices =  122"
##  [5] "Indices =  123" "Indices =  124" "Indices =  125" "Indices =  126"
##  [9] "Indices =  127" "Indices =  128" "Indices =  129" "Indices =  130"
## [13] "Indices =  131" "Indices =  132" "Indices =  133"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 250"         "Concs = 250"         "Concs = 250"        
##  [4] "Concs = 105.2844752" "Concs = 83.9166222"  "Concs = 57.25407999"
##  [7] "Concs = 71.31021926" "Concs = 93.93871253" "Concs = 36.95777127"
## [10] "Concs = 77.4873567"  "Concs = 101.3134582" "Concs = 91.54349597"
## [13] "Concs = 58.38865626" "Concs = 74.14665992" "Concs = 61.1620649" 
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 13 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  130.535247   -0.826428 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 30.2 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -68.785 -23.538   2.232  19.177 119.465 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept) 130.5352  19.5920     6.6627
## Time[ind]    -0.8264   0.3868    -2.1363
## 
## Residual standard error: 30.18 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  130.535247   -0.826428 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  10 2.89 50 75 100 125 150 200 250
##  $ vel: num  74.2 -45.2 258.7 -1332.4 -487.7 ...
##      sub         vel
## 1  10.00    74.15048
## 2   2.89   -45.17618
## 3  50.00   258.66179
## 4  75.00 -1332.37704
## 5 100.00  -487.69647
## 6 125.00 -1608.29494
## 7 150.00 -3206.83717
## 8 200.00 -4132.13800
## 9 250.00 -4132.13998

## Warning in sqrt(diag(varMat)): NaNs produced
## 
## Model fitted: Michaelis-Menten (2 parms)
## 
## Parameter estimates:
## 
##                Estimate Std. Error   t-value p-value
## d:(Intercept) -12885044         NA        NA      NA
## e:(Intercept)    764537          0       Inf       0
## 
## Residual standard error:
## 
##  756.617 (7 degrees of freedom)
## Warning in sqrt(diag(varMat)): NaNs produced

fipsulf

The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.

## [1] "Substrates:"
## [1] "##################################################"
## [1] "Substrate =  10"
##  [1] "Indices =  1"  "Indices =  2"  "Indices =  3"  "Indices =  4" 
##  [5] "Indices =  5"  "Indices =  6"  "Indices =  7"  "Indices =  8" 
##  [9] "Indices =  9"  "Indices =  10" "Indices =  11" "Indices =  12"
## [13] "Indices =  13" "Indices =  14" "Indices =  15"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.226052779" "Concs = 0.249546426" "Concs = 0.249495111"
##  [7] "Concs = 0.556306401" "Concs = 0.629523416" "Concs = 0.545734442"
## [10] "Concs = 1.029532274" "Concs = 1.020828782" "Concs = 1.121529265"
## [13] "Concs = 1.478049545" "Concs = 1.552223152" "Concs = 1.605171177"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
## 0.002836538 0.017390372 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0314 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.089920 -0.016237 -0.002837  0.026473  0.104976 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.0028  0.0154     0.1843
## Time[ind]    0.0174  0.0003    57.2338
## 
## Residual standard error: 0.03141 on 13 degrees of freedom

## (Intercept)   Time[ind] 
## 0.002836538 0.017390372 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  2.89"
##  [1] "Indices =  16" "Indices =  17" "Indices =  18" "Indices =  19"
##  [5] "Indices =  20" "Indices =  21" "Indices =  22" "Indices =  23"
##  [9] "Indices =  24" "Indices =  25" "Indices =  26" "Indices =  27"
## [13] "Indices =  28" "Indices =  29" "Indices =  30"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [7] "Concs = 0.072417652" "Concs = 0.105189206" "Concs = 0.093830232"
## [10] "Concs = 0.446059868" "Concs = 0.501873862" "Concs = 1.937676963"
## [13] "Concs = 0.541481009" "Concs = 0.713021528" "Concs = 0.948269563"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 11 iterations
## 
## Coefficients:
##  (Intercept)    Time[ind] 
## -0.083977895  0.009007886 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.125 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.18525 -0.06610 -0.01371  0.08398  1.48118 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept) -0.0840  0.0551    -1.5251
## Time[ind]    0.0090  0.0011     8.2849
## 
## Residual standard error: 0.1245 on 13 degrees of freedom

##  (Intercept)    Time[ind] 
## -0.083977895  0.009007886 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  50"
##  [1] "Indices =  31" "Indices =  32" "Indices =  33" "Indices =  34"
##  [5] "Indices =  35" "Indices =  36" "Indices =  37" "Indices =  38"
##  [9] "Indices =  39" "Indices =  40" "Indices =  41" "Indices =  42"
## [13] "Indices =  43" "Indices =  44" "Indices =  45"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 2.509901494" "Concs = 0.497072024" "Concs = 0.573048602"
##  [7] "Concs = 0.208702278" "Concs = 1.224307072" "Concs = 0.86186791" 
## [10] "Concs = 2.640613398" "Concs = 2.278728642" "Concs = 1.938091721"
## [13] "Concs = 3.288556396" "Concs = 2.79424236"  "Concs = 2.85277407" 
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.05707229  0.03336470 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.291 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.84931 -0.15850 -0.05707  0.19303  1.95236 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.0571  0.1273     0.4483
## Time[ind]    0.0334  0.0025    13.2724
## 
## Residual standard error: 0.2908 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  0.05707229  0.03336470 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  75"
##  [1] "Indices =  46" "Indices =  47" "Indices =  48" "Indices =  49"
##  [5] "Indices =  50" "Indices =  51" "Indices =  52" "Indices =  53"
##  [9] "Indices =  54" "Indices =  55" "Indices =  56" "Indices =  57"
## [13] "Indices =  58" "Indices =  59"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.61596018"  "Concs = 0.004496637" "Concs = 0.393574273"
##  [7] "Concs = 1.00896852"  "Concs = 1.080335369" "Concs = 1.122428808"
## [10] "Concs = 0.794034486" "Concs = 1.567175192" "Concs = 1.445091993"
## [13] "Concs = 1.567376573" "Concs = 1.397216044"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 10 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.19229663  0.01558037 
## 
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.289 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.42151 -0.19230 -0.09093  0.30944  0.46272 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 0.1923 0.1778     1.0818 
## Time[ind]   0.0156 0.0036     4.3745 
## 
## Residual standard error: 0.2889 on 12 degrees of freedom

## (Intercept)   Time[ind] 
##  0.19229663  0.01558037 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  100"
##  [1] "Indices =  60" "Indices =  61" "Indices =  62" "Indices =  63"
##  [5] "Indices =  64" "Indices =  65" "Indices =  66" "Indices =  67"
##  [9] "Indices =  68" "Indices =  69" "Indices =  70" "Indices =  71"
## [13] "Indices =  72" "Indices =  73" "Indices =  74"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 1.037370756" "Concs = 1.004548869" "Concs = 1.211451943"
##  [7] "Concs = 1.770038982" "Concs = 1.964421756" "Concs = 2.082784287"
## [10] "Concs = 2.421230649" "Concs = 2.716290502" "Concs = 2.511880669"
## [13] "Concs = 2.884476336" "Concs = 3.658963096" "Concs = 3.101044324"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 2 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.45728114  0.03333895 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.463 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.57331 -0.40701  0.05426  0.25638  0.62533 
## 
## Coefficients:
##             Value  Std. Error t value
## (Intercept) 0.4573 0.1723     2.6539 
## Time[ind]   0.0333 0.0034     9.7994 
## 
## Residual standard error: 0.4635 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  0.45728114  0.03333895 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  125"
##  [1] "Indices =  75" "Indices =  76" "Indices =  77" "Indices =  78"
##  [5] "Indices =  79" "Indices =  80" "Indices =  81" "Indices =  82"
##  [9] "Indices =  83" "Indices =  84" "Indices =  85" "Indices =  86"
## [13] "Indices =  87" "Indices =  88" "Indices =  89"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 1.0685532"   "Concs = 1.193964217" "Concs = 1.061157254"
##  [7] "Concs = 1.739690158" "Concs = 1.568026457" "Concs = 1.831902381"
## [10] "Concs = 2.58185903"  "Concs = 2.518118409" "Concs = 2.706182414"
## [13] "Concs = 3.388713261" "Concs = 3.265199632" "Concs = 3.360717697"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.38590066  0.03503517 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.323 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.38590 -0.22611  0.09385  0.18765  0.39495 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.3859  0.1137     3.3954
## Time[ind]    0.0350  0.0022    15.6121
## 
## Residual standard error: 0.3235 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  0.38590066  0.03503517 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  150"
##  [1] "Indices =  90"  "Indices =  91"  "Indices =  92"  "Indices =  93" 
##  [5] "Indices =  94"  "Indices =  95"  "Indices =  96"  "Indices =  97" 
##  [9] "Indices =  98"  "Indices =  99"  "Indices =  100" "Indices =  101"
## [13] "Indices =  102" "Indices =  103" "Indices =  104"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 1.513101462" "Concs = 1.254618226" "Concs = 1.316915121"
##  [7] "Concs = 1.847166036" "Concs = 2.06265471"  "Concs = 2.225655093"
## [10] "Concs = 3.029089226" "Concs = 2.818619179" "Concs = 2.892261352"
## [13] "Concs = 3.395108251" "Concs = 3.493680617" "Concs = 3.346621743"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.57091928  0.03526787 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.519 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.5709 -0.3742  0.1547  0.2802  0.5967 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.5709  0.1714     3.3306
## Time[ind]    0.0353  0.0034    10.4200
## 
## Residual standard error: 0.5188 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  0.57091928  0.03526787 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  200"
##  [1] "Indices =  105" "Indices =  106" "Indices =  107" "Indices =  108"
##  [5] "Indices =  109" "Indices =  110" "Indices =  111" "Indices =  112"
##  [9] "Indices =  113" "Indices =  114" "Indices =  115" "Indices =  116"
## [13] "Indices =  117" "Indices =  118" "Indices =  119"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.921840151" "Concs = 1.265455207" "Concs = 0.083794693"
##  [7] "Concs = 1.758009212" "Concs = 1.131761977" "Concs = 2.14032494" 
## [10] "Concs = 3.119569212" "Concs = 5.219960219" "Concs = 3.68483357" 
## [13] "Concs = 4.382618411" "Concs = 4.121095689" "Concs = 4.42249183" 
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 8 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.13348422  0.04865162 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.245 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.77946 -0.13348 -0.08964  0.28359  2.16738 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.1335  0.2209     0.6041
## Time[ind]    0.0487  0.0044    11.1519
## 
## Residual standard error: 0.2446 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  0.13348422  0.04865162 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate =  250"
##  [1] "Indices =  120" "Indices =  121" "Indices =  122" "Indices =  123"
##  [5] "Indices =  124" "Indices =  125" "Indices =  126" "Indices =  127"
##  [9] "Indices =  128" "Indices =  129" "Indices =  130" "Indices =  131"
## [13] "Indices =  132" "Indices =  133" "Indices =  134"
##  [1] "Times = 0"  "Times = 0"  "Times = 0"  "Times = 15" "Times = 15"
##  [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
##  [1] "Concs = 0"           "Concs = 0"           "Concs = 0"          
##  [4] "Concs = 0.688691412" "Concs = 0.680203691" "Concs = 0.671715969"
##  [7] "Concs = 1.128032043" "Concs = 1.057705208" "Concs = 1.0791266"  
## [10] "Concs = 1.670842039" "Concs = 1.655483305" "Concs = 1.672054571"
## [13] "Concs = 2.11584115"  "Concs = 2.394723427" "Concs = 2.276703681"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
## 
## Coefficients:
## (Intercept)   Time[ind] 
##  0.21108314  0.02380321 
## 
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.179 
## 
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.23753 -0.14388  0.03278  0.11632  0.20285 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  0.2111  0.0635     3.3230
## Time[ind]    0.0238  0.0013    18.9784
## 
## Residual standard error: 0.1787 on 13 degrees of freedom

## (Intercept)   Time[ind] 
##  0.21108314  0.02380321 
##             2.5 % 97.5 %
## (Intercept)    NA     NA
## Time[ind]      NA     NA
## [1] "##################################################"
## 'data.frame':    9 obs. of  2 variables:
##  $ sub: num  10 2.89 50 75 100 125 150 200 250
##  $ vel: num  87 45 166.8 77.9 166.7 ...
##      sub       vel
## 1  10.00  86.95186
## 2   2.89  45.03943
## 3  50.00 166.82351
## 4  75.00  77.90185
## 5 100.00 166.69476
## 6 125.00 175.17585
## 7 150.00 176.33933
## 8 200.00 243.25811
## 9 250.00 119.01603

## 
## Model fitted: Michaelis-Menten (2 parms)
## 
## Parameter estimates:
## 
##                Estimate Std. Error   t-value p-value
## d:(Intercept) 177.90201   27.92410   6.37091  0.0004
## e:(Intercept)  10.95581   11.57501   0.94651  0.3754
## 
## Residual standard error:
## 
##  46.2558 (7 degrees of freedom)

exposure experiment analysis

Results presentation and discussion for parent analytes (atrazine, triadimenon, and fipronil) and their xenobiotic metabolites.

Toxicity of parents and metabolites discussion.

Microsomal analysis of soil and amphibian data for 0 (soil only), 2, 4, 12, 24, and 48 hours after exposure.

Database has factors for time, parent (mapped to analyte), analyte (can be either parent or metabolite), matrix (amphibian or soil), and tank (potentially a nuisance variable).

## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame':  352 obs. of  6 variables:
##  $ time     : int  2 2 2 2 4 4 4 4 12 12 ...
##  $ parent   : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte  : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix   : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
##  $ conc     : num  3.07 3.69 4.7 1.89 7.62 ...
##  $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 4 1 2 3 4 1 2 ...
##  - attr(*, "vars")=List of 4
##   ..$ : symbol parent
##   ..$ : symbol analyte
##   ..$ : symbol matrix
##   ..$ : symbol time
##  - attr(*, "drop")= logi TRUE
##  - attr(*, "indices")=List of 86
##   ..$ : int  0 1 2 3
##   ..$ : int  4 5 6 7
##   ..$ : int  8 9 10 11
##   ..$ : int  12 13 14 15
##   ..$ : int  16 17 18 19
##   ..$ : int  20 21 22 23
##   ..$ : int  24 25 26 27
##   ..$ : int  28 29 30 31
##   ..$ : int  32 33 34 35
##   ..$ : int  36 37 38 39
##   ..$ : int  40 41 42 43
##   ..$ : int  88 89 90 91
##   ..$ : int  92 93 94 95
##   ..$ : int  96 97 98 99
##   ..$ : int  100 101 102 103
##   ..$ : int  104 105 106 107
##   ..$ : int  108 109 110 111
##   ..$ : int  112 113 114 115
##   ..$ : int  116 117 118 119
##   ..$ : int  120 121 122 123
##   ..$ : int  124 125 126 127
##   ..$ : int  128 129 130 131
##   ..$ : int  44 45 46 47
##   ..$ : int  48 49 50 51
##   ..$ : int  52 53 54 55
##   ..$ : int  56 57 58 59
##   ..$ : int  60 61 62 63
##   ..$ : int  64 65 66 67
##   ..$ : int  68 69 70 71
##   ..$ : int  72 73 74 75
##   ..$ : int  76 77 78 79
##   ..$ : int  80 81 82 83
##   ..$ : int  84 85 86 87
##   ..$ : int  264 265 266 267
##   ..$ : int  268 269 270 271
##   ..$ : int  272 273 274 275
##   ..$ : int  276 277 278 279
##   ..$ : int  280 281 282 283
##   ..$ : int  284 285 286 287 288 289 290 291
##   ..$ : int  292 293 294 295
##   ..$ : int  296 297 298 299
##   ..$ : int  300 301 302 303
##   ..$ : int  304 305 306 307
##   ..$ : int  308 309 310 311
##   ..$ : int  312 313 314 315
##   ..$ : int  316 317 318 319
##   ..$ : int  320 321 322 323
##   ..$ : int  324 325 326 327
##   ..$ : int  328 329 330 331 332 333 334 335
##   ..$ : int  336 337 338 339
##   ..$ : int  340 341 342 343
##   ..$ : int  344 345 346 347
##   ..$ : int  348 349 350 351
##   ..$ : int  176 177 178 179
##   ..$ : int  180 181 182 183
##   ..$ : int  184 185 186 187
##   ..$ : int  188 189 190 191
##   ..$ : int  192 193 194 195
##   ..$ : int  196 197 198 199
##   ..$ : int  200 201 202 203
##   ..$ : int  204 205 206 207
##   ..$ : int  208 209 210 211
##   ..$ : int  212 213 214 215
##   ..$ : int  216 217 218 219
##   ..$ : int  220 221 222 223
##   ..$ : int  224 225 226 227
##   ..$ : int  228 229 230 231
##   ..$ : int  232 233 234 235
##   ..$ : int  236 237 238 239
##   ..$ : int  240 241 242 243
##   ..$ : int  244 245 246 247
##   ..$ : int  248 249 250 251
##   ..$ : int  252 253 254 255
##   ..$ : int  256 257 258 259
##   ..$ : int  260 261 262 263
##   ..$ : int  132 133 134 135
##   ..$ : int  136 137 138 139
##   ..$ : int  140 141 142 143
##   ..$ : int  144 145 146 147
##   ..$ : int  148 149 150 151
##   ..$ : int  152 153 154 155
##   ..$ : int  156 157 158 159
##   ..$ : int  160 161 162 163
##   ..$ : int  164 165 166 167
##   ..$ : int  168 169 170 171
##   ..$ : int  172 173 174 175
##  - attr(*, "group_sizes")= int  4 4 4 4 4 4 4 4 4 4 ...
##  - attr(*, "biggest_group_size")= int 8
##  - attr(*, "labels")='data.frame':   86 obs. of  4 variables:
##   ..$ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ analyte: Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
##   ..$ time   : int  2 4 12 24 48 0 2 4 12 24 ...
##   ..- attr(*, "vars")=List of 4
##   .. ..$ : symbol parent
##   .. ..$ : symbol analyte
##   .. ..$ : symbol matrix
##   .. ..$ : symbol time
##   ..- attr(*, "drop")= logi TRUE
## Source: local data frame [352 x 6]
## Groups: parent, analyte, matrix, time [86]
## 
##     time   parent  analyte matrix     conc replicate
##    (int)   (fctr)   (fctr) (fctr)    (dbl)    (fctr)
## 1      2 atrazine atrazine amphib 3.068203         1
## 2      2 atrazine atrazine amphib 3.689640         2
## 3      2 atrazine atrazine amphib 4.701166         3
## 4      2 atrazine atrazine amphib 1.892494         4
## 5      4 atrazine atrazine amphib 7.624610         1
## 6      4 atrazine atrazine amphib 4.134300         2
## 7      4 atrazine atrazine amphib 2.050779         3
## 8      4 atrazine atrazine amphib 7.626486         4
## 9     12 atrazine atrazine amphib 2.452278         1
## 10    12 atrazine atrazine amphib 3.786893         2
## ..   ...      ...      ...    ...      ...       ...
## Source: local data frame [86 x 7]
## Groups: parent, analyte, matrix [?]
## 
##      parent  analyte matrix  time count  ConcMean    ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)     (dbl)     (dbl)
## 1  atrazine atrazine amphib     2     4  3.337876 1.1753225
## 2  atrazine atrazine amphib     4     4  5.359044 2.7518903
## 3  atrazine atrazine amphib    12     4  3.123811 1.2566289
## 4  atrazine atrazine amphib    24     4  1.554919 0.6096102
## 5  atrazine atrazine amphib    48     4  1.001887 0.3545473
## 6  atrazine atrazine   soil     0     4 15.930920 2.5911041
## 7  atrazine atrazine   soil     2     4 19.029034 4.3534303
## 8  atrazine atrazine   soil     4     4 18.770091 2.6953158
## 9  atrazine atrazine   soil    12     4 20.614190 3.8918511
## 10 atrazine atrazine   soil    24     4 24.996196 4.4473828
## ..      ...      ...    ...   ...   ...       ...       ...
## <!-- html table generated in R 3.2.3 by xtable 1.8-2 package -->
## <!-- Mon Mar 14 23:49:21 2016 -->
## <table border=1>
## <tr> <th>  </th> <th> parent </th> <th> analyte </th> <th> matrix </th> <th> time </th> <th> count </th> <th> ConcMean </th> <th> ConcSD </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 3.34 </td> <td align="right"> 1.18 </td> </tr>
##   <tr> <td align="right"> 2 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 5.36 </td> <td align="right"> 2.75 </td> </tr>
##   <tr> <td align="right"> 3 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 3.12 </td> <td align="right"> 1.26 </td> </tr>
##   <tr> <td align="right"> 4 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 1.55 </td> <td align="right"> 0.61 </td> </tr>
##   <tr> <td align="right"> 5 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 1.00 </td> <td align="right"> 0.35 </td> </tr>
##   <tr> <td align="right"> 6 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 15.93 </td> <td align="right"> 2.59 </td> </tr>
##   <tr> <td align="right"> 7 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 19.03 </td> <td align="right"> 4.35 </td> </tr>
##   <tr> <td align="right"> 8 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 18.77 </td> <td align="right"> 2.70 </td> </tr>
##   <tr> <td align="right"> 9 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 20.61 </td> <td align="right"> 3.89 </td> </tr>
##   <tr> <td align="right"> 10 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 25.00 </td> <td align="right"> 4.45 </td> </tr>
##   <tr> <td align="right"> 11 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 26.43 </td> <td align="right"> 4.38 </td> </tr>
##   <tr> <td align="right"> 12 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 13 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
##   <tr> <td align="right"> 14 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.05 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 15 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 16 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 17 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 18 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 19 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 20 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 21 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 22 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 23 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.33 </td> <td align="right"> 0.12 </td> </tr>
##   <tr> <td align="right"> 24 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.94 </td> <td align="right"> 0.76 </td> </tr>
##   <tr> <td align="right"> 25 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 1.08 </td> <td align="right"> 0.51 </td> </tr>
##   <tr> <td align="right"> 26 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 1.99 </td> <td align="right"> 1.35 </td> </tr>
##   <tr> <td align="right"> 27 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.66 </td> <td align="right"> 0.53 </td> </tr>
##   <tr> <td align="right"> 28 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 29 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> -0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 30 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 31 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.07 </td> </tr>
##   <tr> <td align="right"> 32 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
##   <tr> <td align="right"> 33 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.06 </td> </tr>
##   <tr> <td align="right"> 34 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 1.87 </td> <td align="right"> 1.35 </td> </tr>
##   <tr> <td align="right"> 35 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 1.30 </td> <td align="right"> 0.52 </td> </tr>
##   <tr> <td align="right"> 36 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.57 </td> <td align="right"> 0.24 </td> </tr>
##   <tr> <td align="right"> 37 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.27 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 38 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.21 </td> <td align="right"> 0.13 </td> </tr>
##   <tr> <td align="right"> 39 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   8 </td> <td align="right"> 0.41 </td> <td align="right"> 0.45 </td> </tr>
##   <tr> <td align="right"> 40 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.24 </td> </tr>
##   <tr> <td align="right"> 41 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.82 </td> <td align="right"> 0.17 </td> </tr>
##   <tr> <td align="right"> 42 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.70 </td> <td align="right"> 0.11 </td> </tr>
##   <tr> <td align="right"> 43 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.36 </td> <td align="right"> 0.06 </td> </tr>
##   <tr> <td align="right"> 44 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.35 </td> <td align="right"> 0.29 </td> </tr>
##   <tr> <td align="right"> 45 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.40 </td> <td align="right"> 0.48 </td> </tr>
##   <tr> <td align="right"> 46 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.61 </td> <td align="right"> 0.57 </td> </tr>
##   <tr> <td align="right"> 47 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 1.25 </td> <td align="right"> 0.53 </td> </tr>
##   <tr> <td align="right"> 48 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.91 </td> <td align="right"> 0.57 </td> </tr>
##   <tr> <td align="right"> 49 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   8 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 50 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 51 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 52 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 53 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 54 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 55 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 56 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 57 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 58 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 59 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 60 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 61 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 62 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 63 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 64 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 65 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 66 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.13 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 67 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
##   <tr> <td align="right"> 68 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 69 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.03 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 70 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 71 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 72 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 73 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> 74 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 75 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 76 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 0.39 </td> <td align="right"> 0.08 </td> </tr>
##   <tr> <td align="right"> 77 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 0.55 </td> <td align="right"> 0.30 </td> </tr>
##   <tr> <td align="right"> 78 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 0.75 </td> <td align="right"> 0.32 </td> </tr>
##   <tr> <td align="right"> 79 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.86 </td> </tr>
##   <tr> <td align="right"> 80 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 0.25 </td> <td align="right"> 0.08 </td> </tr>
##   <tr> <td align="right"> 81 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">   0 </td> <td align="right">   4 </td> <td align="right"> 3.11 </td> <td align="right"> 0.85 </td> </tr>
##   <tr> <td align="right"> 82 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">   2 </td> <td align="right">   4 </td> <td align="right"> 3.66 </td> <td align="right"> 1.34 </td> </tr>
##   <tr> <td align="right"> 83 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">   4 </td> <td align="right">   4 </td> <td align="right"> 5.28 </td> <td align="right"> 0.37 </td> </tr>
##   <tr> <td align="right"> 84 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">  12 </td> <td align="right">   4 </td> <td align="right"> 5.93 </td> <td align="right"> 1.00 </td> </tr>
##   <tr> <td align="right"> 85 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">  24 </td> <td align="right">   4 </td> <td align="right"> 4.82 </td> <td align="right"> 0.32 </td> </tr>
##   <tr> <td align="right"> 86 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right">  48 </td> <td align="right">   4 </td> <td align="right"> 4.18 </td> <td align="right"> 0.44 </td> </tr>
##    </table>

The amphibian data set summary statistics. Atrazine peaks at 4 hours and then declines monotonically. DEA peaks at 12 hours and DIA at 24. Fipronil steadily declines from its first observation at 2 hours with fipronil sulfone not peaking until 24 hours. Triadimenon peaks at 24 hours with its metabolites tdla and tdlb peaking at 4 hours.

## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame':  86 obs. of  7 variables:
##  $ parent  : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ matrix  : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
##  $ time    : int  2 4 12 24 48 0 2 4 12 24 ...
##  $ count   : int  4 4 4 4 4 4 4 4 4 4 ...
##  $ ConcMean: num  3.34 5.36 3.12 1.55 1 ...
##  $ ConcSD  : num  1.175 2.752 1.257 0.61 0.355 ...
##  - attr(*, "vars")=List of 3
##   ..$ : symbol parent
##   ..$ : symbol analyte
##   ..$ : symbol matrix
##  - attr(*, "drop")= logi TRUE
## Source: local data frame [6 x 7]
## Groups: parent, analyte, matrix [2]
## 
##     parent  analyte matrix  time count   ConcMean     ConcSD
##     (fctr)   (fctr) (fctr) (int) (int)      (dbl)      (dbl)
## 1 atrazine atrazine amphib     2     4 3.33787563 1.17532253
## 2 atrazine atrazine amphib     4     4 5.35904387 2.75189034
## 3 atrazine atrazine amphib    12     4 3.12381130 1.25662887
## 4 atrazine atrazine amphib    24     4 1.55491895 0.60961016
## 5 atrazine atrazine amphib    48     4 1.00188749 0.35454734
## 6 atrazine      dea amphib     2     4 0.01389877 0.00522407
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
## 
##      parent  analyte matrix  time count   ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)      (dbl)      (dbl)
## 1  atrazine atrazine amphib     2     4 3.33787563 1.17532253
## 2  atrazine atrazine amphib     4     4 5.35904387 2.75189034
## 3  atrazine atrazine amphib    12     4 3.12381130 1.25662887
## 4  atrazine atrazine amphib    24     4 1.55491895 0.60961016
## 5  atrazine atrazine amphib    48     4 1.00188749 0.35454734
## 6  atrazine      dea amphib     2     4 0.01389877 0.00522407
## 7  atrazine      dea amphib     4     4 0.04436711 0.02843181
## 8  atrazine      dea amphib    12     4 0.05402182 0.01282235
## 9  atrazine      dea amphib    24     4 0.03652473 0.01310278
## 10 atrazine      dea amphib    48     4 0.01951501 0.01958540
## 11 atrazine      dia amphib     2     4 0.32878185 0.12495746
## 12 atrazine      dia amphib     4     4 0.94192818 0.76074427
## 13 atrazine      dia amphib    12     4 1.08350960 0.50576827
## 14 atrazine      dia amphib    24     4 1.98835970 1.34925248
## 15 atrazine      dia amphib    48     4 0.66238821 0.53051448
## [1] "atrazine"
## [1] "dea"
## [1] "dia"
## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
## 
##      parent  analyte matrix  time count  ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)     (dbl)      (dbl)
## 1  fipronil fipronil amphib     2     4 1.8670398 1.34631230
## 2  fipronil fipronil amphib     4     4 1.3005836 0.52188454
## 3  fipronil fipronil amphib    12     4 0.5659565 0.24026633
## 4  fipronil fipronil amphib    24     4 0.2676732 0.05106111
## 5  fipronil fipronil amphib    48     4 0.2119504 0.13140536
## 6  fipronil  fipsulf amphib     2     4 0.3465734 0.28711156
## 7  fipronil  fipsulf amphib     4     4 0.3966089 0.47739157
## 8  fipronil  fipsulf amphib    12     4 0.6129114 0.57346517
## 9  fipronil  fipsulf amphib    24     4 1.2528179 0.52648677
## 10 fipronil  fipsulf amphib    48     4 0.9067126 0.56596417
## Source: local data frame [0 x 7]
## Groups: parent, analyte, matrix [0]
## 
## Variables not shown: parent (fctr), analyte (fctr), matrix (fctr), time
##   (int), count (int), ConcMean (dbl), ConcSD (dbl)

The soil data set summary statistics. Atrazine in soil showing an upwards trend (need to test if significant) with dia and dea levels very low indicating little degradation in soil over the 48 hour period. Fipronil and triadimenon data also indicating little degradation in soil.

## Source: local data frame [18 x 7]
## Groups: parent, analyte, matrix [3]
## 
##      parent  analyte matrix  time count     ConcMean      ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)        (dbl)       (dbl)
## 1  atrazine atrazine   soil     0     4 15.930919692 2.591104068
## 2  atrazine atrazine   soil     2     4 19.029034412 4.353430337
## 3  atrazine atrazine   soil     4     4 18.770091080 2.695315758
## 4  atrazine atrazine   soil    12     4 20.614190363 3.891851074
## 5  atrazine atrazine   soil    24     4 24.996195532 4.447382801
## 6  atrazine atrazine   soil    48     4 26.434744900 4.377099498
## 7  atrazine      dea   soil     0     4  0.000000000 0.000000000
## 8  atrazine      dea   soil     2     4  0.001570429 0.000633009
## 9  atrazine      dea   soil     4     4  0.002999216 0.001537652
## 10 atrazine      dea   soil    12     4  0.005469015 0.004234880
## 11 atrazine      dea   soil    24     4  0.007308439 0.001736211
## 12 atrazine      dea   soil    48     4  0.008784632 0.003772339
## 13 atrazine      dia   soil     0     4  0.000000000 0.000000000
## 14 atrazine      dia   soil     2     4 -0.007727286 0.007374085
## 15 atrazine      dia   soil     4     4  0.020538600 0.020166308
## 16 atrazine      dia   soil    12     4  0.077036921 0.067772652
## 17 atrazine      dia   soil    24     4  0.042975804 0.030007793
## 18 atrazine      dia   soil    48     4  0.063693292 0.058241606
## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
## 
##      parent  analyte matrix  time count   ConcMean      ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)      (dbl)       (dbl)
## 1  fipronil fipronil   soil     2     8 0.40768123 0.447265792
## 2  fipronil fipronil   soil     4     4 0.86826316 0.244191727
## 3  fipronil fipronil   soil    12     4 0.81738069 0.169691335
## 4  fipronil fipronil   soil    24     4 0.70225877 0.108745058
## 5  fipronil fipronil   soil    48     4 0.35560948 0.058543752
## 6  fipronil  fipsulf   soil     2     8 0.01022479 0.012898421
## 7  fipronil  fipsulf   soil     4     4 0.02193831 0.010765665
## 8  fipronil  fipsulf   soil    12     4 0.01829893 0.005013814
## 9  fipronil  fipsulf   soil    24     4 0.01917848 0.009139211
## 10 fipronil  fipsulf   soil    48     4 0.01262887 0.005517408
## Source: local data frame [0 x 7]
## Groups: parent, analyte, matrix [0]
## 
## Variables not shown: parent (fctr), analyte (fctr), matrix (fctr), time
##   (int), count (int), ConcMean (dbl), ConcSD (dbl)
pdf(paste(micro.graphics,"data_mean_scatterplot",".pdf", sep=""))
  par(mfrow=c(3,1))
  print(parents)
## [1] atrazine    triadimefon fipronil   
## Levels: atrazine fipronil triadimefon
  for(parent in parents){
    i=0
    print(parent)
    temp.parent <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
    print(temp.parent)
    parent.analytes <- unique(temp.parent$analyte)
    for(analyte in parent.analytes){
      print(parent)
      print(analyte) 
      analytetemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$analyte==analyte),]
      xvalues <- as.numeric(as.character(analytetemp$time))
      points.y <- micro.amphib[which(micro.amphib$analyte==analyte),]$conc
      points.x <- as.numeric(as.character(micro.amphib[which(micro.amphib$analyte==analyte),]$time))
      #create empty plot if needed
      if(i==0){
        parenttemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
        maxconc <- max(points.y) 
        plot(xvalues,analytetemp$ConcMean,type="l", xlim=c(0,48),
             ylim = c(0,maxconc), main=parent,col="black", xlab="Hours", ylab="Concentration")
        axis(1,at=xvalues)
        i=1
      }
      #add line for parent metabolite
      if(analyte %in% parents){
        lines(xvalues,analytetemp$ConcMean,type="l",col="red")
        points(points.x, points.y, col = "red")
      }else{
      #add line for daughter metabolite
        lines(xvalues,analytetemp$ConcMean,type="l",col="blue")
        points(points.x, points.y, col = "blue")
      }
    }
  }
## [1] "atrazine"
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
## 
##      parent  analyte matrix  time count   ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)      (dbl)      (dbl)
## 1  atrazine atrazine amphib     2     4 3.33787563 1.17532253
## 2  atrazine atrazine amphib     4     4 5.35904387 2.75189034
## 3  atrazine atrazine amphib    12     4 3.12381130 1.25662887
## 4  atrazine atrazine amphib    24     4 1.55491895 0.60961016
## 5  atrazine atrazine amphib    48     4 1.00188749 0.35454734
## 6  atrazine      dea amphib     2     4 0.01389877 0.00522407
## 7  atrazine      dea amphib     4     4 0.04436711 0.02843181
## 8  atrazine      dea amphib    12     4 0.05402182 0.01282235
## 9  atrazine      dea amphib    24     4 0.03652473 0.01310278
## 10 atrazine      dea amphib    48     4 0.01951501 0.01958540
## 11 atrazine      dia amphib     2     4 0.32878185 0.12495746
## 12 atrazine      dia amphib     4     4 0.94192818 0.76074427
## 13 atrazine      dia amphib    12     4 1.08350960 0.50576827
## 14 atrazine      dia amphib    24     4 1.98835970 1.34925248
## 15 atrazine      dia amphib    48     4 0.66238821 0.53051448
## [1] "atrazine"
## [1] "atrazine"
## [1] "atrazine"
## [1] "dea"
## [1] "atrazine"
## [1] "dia"
## [1] "triadimefon"
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
## 
##         parent     analyte matrix  time count   ConcMean      ConcSD
##         (fctr)      (fctr) (fctr) (int) (int)      (dbl)       (dbl)
## 1  triadimefon        tdla amphib     2     4 0.05514470 0.021089764
## 2  triadimefon        tdla amphib     4     4 0.08150175 0.046221502
## 3  triadimefon        tdla amphib    12     4 0.03632384 0.015222899
## 4  triadimefon        tdla amphib    24     4 0.02400790 0.007522554
## 5  triadimefon        tdla amphib    48     4 0.01549908 0.004845715
## 6  triadimefon        tdlb amphib     2     4 0.08362714 0.016364595
## 7  triadimefon        tdlb amphib     4     4 0.13009543 0.054315693
## 8  triadimefon        tdlb amphib    12     4 0.07664673 0.048553355
## 9  triadimefon        tdlb amphib    24     4 0.04183235 0.011652266
## 10 triadimefon        tdlb amphib    48     4 0.02950214 0.003438978
## 11 triadimefon triadimefon amphib     2     4 0.38678831 0.075852995
## 12 triadimefon triadimefon amphib     4     4 0.54862458 0.300394386
## 13 triadimefon triadimefon amphib    12     4 0.75491439 0.318237965
## 14 triadimefon triadimefon amphib    24     4 0.86540039 0.860421208
## 15 triadimefon triadimefon amphib    48     4 0.24868748 0.079848623
## [1] "triadimefon"
## [1] "tdla"
## [1] "triadimefon"
## [1] "tdlb"
## [1] "triadimefon"
## [1] "triadimefon"
## [1] "fipronil"
## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
## 
##      parent  analyte matrix  time count  ConcMean     ConcSD
##      (fctr)   (fctr) (fctr) (int) (int)     (dbl)      (dbl)
## 1  fipronil fipronil amphib     2     4 1.8670398 1.34631230
## 2  fipronil fipronil amphib     4     4 1.3005836 0.52188454
## 3  fipronil fipronil amphib    12     4 0.5659565 0.24026633
## 4  fipronil fipronil amphib    24     4 0.2676732 0.05106111
## 5  fipronil fipronil amphib    48     4 0.2119504 0.13140536
## 6  fipronil  fipsulf amphib     2     4 0.3465734 0.28711156
## 7  fipronil  fipsulf amphib     4     4 0.3966089 0.47739157
## 8  fipronil  fipsulf amphib    12     4 0.6129114 0.57346517
## 9  fipronil  fipsulf amphib    24     4 1.2528179 0.52648677
## 10 fipronil  fipsulf amphib    48     4 0.9067126 0.56596417
## [1] "fipronil"
## [1] "fipronil"
## [1] "fipronil"
## [1] "fipsulf"
dev.off()
## quartz_off_screen 
##                 2

la de da

turn times series to zoo objects

estimate lambdas using maximum likelihood for each time series

library(maxLik)

MLexp <- function(times, data){

expLik <- function(param) { y <- data t <- times alpha1 <- param[1] lambda1 <- param[2]-1(alpha1-lambda1t) - y/(exp(alpha1-lambda1*t)) }

max.fit <- maxLik(expLik, start = c(1,1)) crit <- qt(.975, length(data)-2) max.intercept.CI <- c(summary(max.fit)\(est[1,1]-crit*summary(max.fit)\)est[1,2],summary(max.fit)\(est[1,1]+crit*summary(max.fit)\)est[1,2]) max.decayrate.CI <- c(-1summary(max.fit)\(est[2,1]-crit*summary(max.fit)\)est[2,2],-1summary(max.fit)\(est[2,1]+crit*summary(max.fit)\)est[2,2]) max.halflife.CI <- c(log(2)/max.decayrate.CI[2],log(2)/max.decayrate.CI[1])

paste(“MLE for Initial Concentration =”,max.fit\(est[1], "MLE for decay rate =", max.fit\)est[2], “MLE for half life =”, -log(.5)/max.fit$est[2])

temp.list <- list(max.fit\(est[1], max.fit\)est[2], -log(.5)/max.fit$est[2], max.intercept.CI, max.decayrate.CI, max.halflife.CI, vcov(max.fit) ) return(temp.list) }

MLexp.intercept <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[1]] }

MLexp.decayrate <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[2]] }

MLexp.halflife <- function(times,data) { temp.fit <- MLexp(times,data) temp.fit[[3]] }

MLexp.intercept.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[4]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }

MLexp.decayrate.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[5]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }

MLexp.halflife.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[6]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }

microsome experiment analysis

data in csv format